Math Pi Euler

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These are questions asked by Math Pi Euler

Hi all, I am having the follwing DE:

restart: 
(diff(z(x), x, x))-z(x) - cos(2*x)/(1+delta*z(x)) = 0:

With initial conditions: z(-pi/4)=z(pi/4)=0 and |delta|<<1

I showed by hand by using perturbation theory the second order approximation. The hint was: you can use Maple to check your answer. 

Is there somebody who can help me with this?

 

 

Hi all, I wish to solve in Maple 4 equations with 4 unknowns. I do exactly what is in the example, but Maple produces an error. Perhaps someone can see, where I make the mistake.

restart:
G1:=a*x^3 + b*x^2:
G2:=c*(x-1)^3 +d*(x-1)^2:
eq1:=subs(x=u, G1=G2):
eq2:=subs(x=u, diff(G2,x)-diff(G1,x)):
eq3:=subs(x=u, diff(G2,x$2)-diff(G1,x$2)):
eq4:=subs(x=u, diff(G2,x$3)-diff(G1,x$3)):
sol:=solve({eq1=0, eq2=0, eq3=0, eq4=1},{a,b,c,d});
Error, invalid input: solve expects its 1st argument, eqs, to be of type {`and`, `not`, `or`, algebraic, relation(algebraic), ({list, set})({`and`, `not`, `or`, algebraic, relation(algebraic)})}, but received {6*c-6*a = 1, 6*c*(u-1)+2*d-6*a*u-2*b = 0, 3*c*(u-1)^2+2*d*(u-1)-3*a*u^2-2*b*u = 0, (a*u^3+b*u^2 = c*(u-1)^3+d*(u-1)^2) = 0}

 

Hi all, since I cannot use Latex over here I try to formulate as good as possible. Suppose we have the standard integral from a to b of a function f(x), which is equal to:

h * sum (k=1 to N) [ck f(a+kh)] +O(hp), where h=(b-a)/N+1, an p(N)>= N+1;

Would it be possible to write a procedure to evaluate the coefficients ck , k=1,2,3..N and P(N)

Perhaps a stupid question, because I don't know if it is possible.

Best wishes, Math

Dear all, I've been given the following procedure:

> int_part:=proc(f,h,n::integer) local k,u,v,s;
     > u:=f;
     > v:=h;
     > s:=0;
     > for k from 1 to n do;
     > u:=int(u,t);
     > s:=s-(-1)^(k)*u*v;
     > v:=diff(v,t);

> od;
> s; end: 

To apply on the following function: f:=int((exp(-x*t))/sqrt(t(t+1)),t=1..infinity);

And f is a function of x. F(x).

It should give the asymptotic expansion up to O(x^-6). But probably I do something wrong. Can somebody help me please?

Best wishes, Math

The real function y(x) is defined implicitly by the equation:

ln(1+x)*y) + e^((x^2)*(y^2)) = x + cos(x);

How can I find y(0) = 1 and the values of the first six derivatives y(k)(0), k=1, 2,..6 at x=0 to show the Taylorseries about x=0?

(I started by defining p:= ln(1+x)*y) + e^((x^2)*(y^2)) - x - cos(x), but that went wrong. 

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