Items tagged with dsolve

Hello friends!

I have one question, whenever I solved system of ODEs using numerical solution (bilton command i.e., dsolve(dsys1, numeric, output = listprocedure, range = 0 .. 1)), its accutacy always like 10 or 12 digits not above at all. I want to how i improve the accuracy. I am waiting your postive answer.


Can somebody help me to find out why Maple can't completely solve this system of differential equations?

The answer to the previous command is

but I don't get the solution for u(x). This should be u(x)=-x+x^2/2.

Thanks for your help


If algebra use factorise method,

Which method do maple use to dsolve differential equation?


Respected member!
Please help me to find the solution of attached problem.


> subject to boundary conditions






alpha := evalf(2*Pi*(1/180)); EP := .2; lambda := .1; HA := 5; RE := 20

ODEforNum := (1+EP)*(((D@@3)(F))(r)+4*alpha^2*(D(F))(r))+2*alpha*RE*F(r)*(D(F))(r)-HA*alpha^2*(D(F))(r)-3*EP*lambda*((1/2)*(D(F))(r)^2*((D@@3)(F))(r)+(D(F))(r)*((D@@2)(F))(r)^2)/alpha^2-EP*lambda*(72*F(r)^2*(D(F))(r)+2*(D(F))(r)^3+32*F(r)*(D(F))(r)*((D@@2)(F))(r)+2*F(r)^2*((D@@3)(F))(r)) = 0

1.2*((D@@3)(F))(r)-0.243693936e-3*(D(F))(r)+1.396263402*F(r)*(D(F))(r)-24.62104762*(D(F))(r)^2*((D@@3)(F))(r)-49.24209525*(D(F))(r)*((D@@2)(F))(r)^2-1.44*F(r)^2*(D(F))(r)-0.4e-1*(D(F))(r)^3-.64*F(r)*(D(F))(r)*((D@@2)(F))(r)-0.4e-1*F(r)^2*((D@@3)(F))(r) = 0



BCSforNum := F(0) = 1, (D(F))(0) = 0, F(1) = 0

Digits := 15



numsol := dsolve({BCSforNum, ODEforNum}, numeric, output = listprocedure)

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging










Respected member!
Please help me to find the solution of attached problem,  I am a new user so please forgive any

Dear friends:

I am facing two problems

1. one is to get solution of the below system of ODE for L=100 (highlited as red) and

2. the other is I want the graph in the form of solid line not poit, asterisk etc.


restart; epsilon := .1; Pr := 1; beta := .1; Sc := 1; S := 1; L := 20;
for i from -L while i <= L do;
a[i] := 1.0*i/L;
end do;
for i2 from -L while i2 <= L do;

fw := a[i2]; 

Eq1[i2] := eval(diff(F(eta), eta, eta, eta)+F(eta)*(diff(F(eta), eta, eta))-(diff(F(eta), eta))^2+S*(epsilon-(diff(F(eta), eta)))+epsilon^2);
Eq2[i2] := eval((diff(G(eta), eta, eta))/Pr-G(eta)*(diff(F(eta), eta))+F(eta)*(diff(G(eta), eta))); 
Eq3[i2] := eval(diff(H(eta), eta, eta)+Sc*(F(eta)*(diff(H(eta), eta))-beta*H(eta)));
IC[i2] := F(0) = a[i2], (D(F))(0) = 1, (D(F))(L) = epsilon, G(0) = 1, G(L) = 0, H(0) = 1, H(L) = 0;
dsys1[i2] := {Eq1[i2], Eq2[i2], Eq3[i2], IC[i2]};
dsol1[i2] := dsolve(dsys1[i2], numeric, output = listprocedure, range = 0 .. L);
dsol1x[i2] := subs(dsol1[i2], diff(F(eta), eta, eta));
dsol1y[i2] := subs(dsol1[i2], G(eta));
dsol1z[i2] := subs(dsol1[i2], H(eta)) end do;

for j from -L while j <= L do; 
g[j] := eval(-dsol1x[j](0)) end do;

g6 := pointplot({seq([n/L, g[n]], n = -L .. L)}, symbol = asterisk, symbolsize = 15, color = red);

Please see the problem and correct as soon as possible. I am waiting your positive respone.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China


How I can solve it for P?

P=i^(2)r+(&DifferentialD;)/(&DifferentialD; t) (1/(2)l(tetha)i^(2))+1/(2)i^(2)(&DifferentialD;l(tetha))/(&DifferentialD; theta) w

attach i(t) "corrente", l(t) "induttanza", theta "angular", w "rotary speed"graph of funtions


I get no output from the following

deqv := m*v(s)*(diff(v(s), s)) = m*g-k*v(s)^2

I have to write

solv := `assuming`([dsolve({deqv, v(0) = v__0}, v(s), implicit)], [v__0 > 0])

in order to get

-g*m/k-exp(-2*k*s/m)*(-g*m/k+v__0^2)+v(s)^2 = 0

and then I have to write my own function

It should be a piece of cake for maple to solve this!








I'm trying to plot the velocity of a ball thrown upwards with air resistance proportional to v^2 and also some simpler forms of this.

But the solution to v^2 returns root of and the plot stops for some specific time value. How can I proceed this plot to let's say 10 sec?







deq1 := m*(diff(v(t), t)) = -m*g:


sol := dsolve({deq1, v(0) = v__0}, v(t))

v(t) = -g*t+v__0


V := unapply(rhs(sol), t):




deq2 := m*(diff(v2(t), t)) = -m*g-k*v2(t):


sol2 := dsolve({deq2, v2(0) = v__0}, v2(t))

v2(t) = -g*m/k+exp(-k*t/m)*(v__0+g*m/k)


V2 := unapply(rhs(sol2), t):


deq3 := m*(diff(v3(t), t)) = -m*g-k*v3(t)*abs(v3(t))

m*(diff(v3(t), t)) = -m*g-k*v3(t)*abs(v3(t))


sol3 := dsolve({deq3, v3(0) = v__0}, v3(t))

v3(t) = RootOf(t+m*piecewise(_Z <= 0, arctanh(k*_Z/(k*m*g)^(1/2))/(k*m*g)^(1/2), 0 < _Z, arctan(k*_Z/(k*m*g)^(1/2))/(k*m*g)^(1/2))-m*piecewise(v__0 <= 0, arctanh(k*v__0/(k*m*g)^(1/2))/(k*m*g)^(1/2), 0 < v__0, arctan(k*v__0/(k*m*g)^(1/2))/(k*m*g)^(1/2)))


V3 := unapply(rhs(sol3), t):


m := 0.258e-2:


plot([V(t), V2(t), V3(t)], t = 0 .. 5, color = [blue, red, black], gridlines = true)





I am not a math major, so may be I am missing something here. But for this ode:

(diff(y(x),x))^2=4 * y(x)

There ought to be (I think) 2 solutions (other than the singular one y(x)=0), due to the square root. i.e the ode becomes

   diff(y(x),x)= +-  2* sqrt(y(x))

So for the + case, there is one solution, and for the - case, there is another solution. But Maple dsolve only gives one solution (again, ignoring the singular solution for now):

eq:=(diff(y(x),x))^2=4 * y(x);

     y(x) = _C1^2-2*_C1*x+x^2

In Mathematica, it gives both solutions

ode = (y'[x])^2 == 4 y[x];
DSolve[ode, y[x], x] // Simplify
    {  {y[x] -> (1/4)*(-2*x + C[1])^2},   {y[x] -> (1/4)*(2*x + C[1])^2}}

Both Maple and Mathematica solutions are correct ofcourse. But my question is why did not Maple give both (non-singular) solutions? and it only gave one?

Maple 2016.2





why this equation does not any answer?




eq:={-J*g[1]*(diff(w(x), x, x, x, x, x, x))+J*c[1]*(diff(w(x), x, x, x, x))+A*g[113113]*(diff(w(x), x, x, x, x))+(beta[11]*A*0)*`&Delta;T`*(diff(w(x), x, x))+2*b*f[1133]*(Pi/L)^2*(d[33]*lambda[3]*`&Delta;T`*L/mu[33]-2*f[1133]*a*Pi/L-P[3]*`&Delta;T`*L)*sin(Pi*x/L)*sinh(h*Pi/(2*L))/(2*cosh(h*Pi/(2*L))*(-a33+d[33]^2/mu[33])) = 0, w(0) = 0, w(L) = 0, (D(w))(0) = 0, (D(w))(L) = 0, ((D@@3)(w))(0) = 0, ((D@@3)(w))(L) = 0}

{-J*g[1]*(diff(diff(diff(diff(diff(diff(w(x), x), x), x), x), x), x))+J*c[1]*(diff(diff(diff(diff(w(x), x), x), x), x))+A*g[113113]*(diff(diff(diff(diff(w(x), x), x), x), x))+b*f[1133]*Pi^2*(d[33]*lambda[3]*`&Delta;T`*L/mu[33]-2*f[1133]*a*Pi/L-P[3]*`&Delta;T`*L)*sin(Pi*x/L)*sinh((1/2)*h*Pi/L)/(L^2*cosh((1/2)*h*Pi/L)*(-a33+d[33]^2/mu[33])) = 0, w(0) = 0, w(L) = 0, (D(w))(0) = 0, (D(w))(L) = 0, ((D@@3)(w))(0) = 0, ((D@@3)(w))(L) = 0}


dsolve(eq, w(x))





The ODE diff(y(x),x) = sec(x)^2*sec(y(x))^3  can be solved as separable. So the answer should be 


as can be seen by direct integration of each side of the differential equation. I am trying to make Maple give the same answer, but not having any luck. 

ode:=diff(y(x),x) = sec(x)^2*sec(y(x))^3;
sol:=dsolve(ode, y(x),implicit);

I tried simplify(sol,trig) and tried simplify(sol,size).  Both Maple answer, and the simple answer solve the ODE.

Is there a way to make Maple dsolve give the simpler answer, or simplify/convert the answer it gives to the simpler one? I am newbie in Maple.

I was trying to solve a system of ODE using Maple, but to my surprise, Maple recognizes diff((phi(t), t)) as a variable which is different than t. 

My code is as following:

dsys := {2*m1*(a+l*sin(phi(t)))^2*(diff(diff(theta(t), t), t))+4*m1*(a+l*sin(phi(t)))*l*cos(phi(t))*(diff(theta(t), t))*(diff(phi(t), t)) = M, 2*m1*l^2*(diff(diff(phi(t), t), t))+4*m2*l^2*sin(2*phi(t))*(diff(phi(t), t))*(diff(phi(t), t))+4*m2*l^2*sin(phi(t))^2*(diff(diff(phi(t), t), t))-2*m1*(a+l*sin(phi(t)))*l*cos(phi(t))*(diff(theta(t), t))*(diff(theta(t), t))-2*m2*l^2*(sin(2*phi(t)))(diff(phi(t), t))*(diff(phi(t), t)) = -(2*(m1+m2))*g*l*sin(phi(t))-2*k*l^2*sin(2*phi(t)), phi(0) = 0, theta(0) = 0, (D(phi))(0) = 0, (D(theta))(0) = 0}

subs({M = 10, a = .5, g = 9.81, k = .1, l = .5, m1 = 10, m2 = 1}, dsys);

dsn1 := dsolve(dsys, numeric)

The error I got was Error, (in dsolve/numeric/process_input) input system must be an ODE system, got independent variables {t, diff(phi(t), t)}

I don't get why this is happening. Could you show me what's going on?

Hello; I found another ODE which Maple gives division by zero on.  Is this also a bug? 

dsolve(x*(a^2*x+(x^2-y(x)^2)*y(x))*diff(y(x),x)^2-(2*a^2*x*y(x)-(x^2-y(x)^2)^2)*diff(y(x),x)+a^2*y(x)^2-x*y(x)*(x^2-y(x)^2) = 0, y(x));

Error, (in dsolve) numeric exception: division by zero

This is from a book. Using Maple 2016.1 on windows.

Maple 2016.1 on windows. This ODE from a book, and Maple gives division by zero. Is this a bug or expected?

ode:=(a^2*x+(x^2-y(x)^2)*y(x))*diff(y(x),x)+x*(x^2-y(x)^2) = a^2*y(x);
dsolve(ode, y(x));

Error, (in dsolve) numeric exception: division by zero

Mathematica gives this to same ODE, but no division by zero.

DSolve[x*(x^2 - y[x]^2) + (a^2*x + y[x]*(x^2 - y[x]^2))*y'[x] == a^2*y[x], y[x], x]

Solve[x^2/2 - (1/2)*a^2*Log[x - y[x]] + (1/2)*a^2*Log[x + y[x]] +y[x]^2/2 == C[1], y[x]]

Where is the division by zero coming from in Maple?

2016.1 on windows.

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