## 874 Reputation

15 years, 46 days

## ?plots[pointplot] or ?plot[pointplot3d]...

Try:

`plots[pointplot]( [seq([i,S[i]],i=1..numelems(S))], style=line);`

## One parameter....

You are missing a condition, so it acts like a parameter.

Example:

```dsys := {diff(s(x), x, x, x)+(1/2)*s(x)*(diff(s(x), x, x)) = 0, s(0) = 0, (D(s))(5) = 1}; other:=seq({D(s)(0)=i/10}, i=-8..1);; sol:=seq(dsolve(dsys union cond,numeric), cond=[other]); plots[display](map(plots[odeplot], [sol], 0..5));```

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## Like this:...

```restart; PDEtools[declare](f(x), prime = x);```

```N := 4; F := sum(p^i*f[i](x), i = 0 .. N); HPMEq := (1 - p)*(diff(F, `\$`(x, 3))) + p*((diff(F, `\$`(x, 3))) + 1/2*(diff(F, x, x))*F); for i from 0 to N do equ[2][i] := coeff(HPMEq, p, i) = 0 end do;```

```cond[1][0] := f[0](0) = 0, (D(f[0]))(0) = 0, (D(f[0]))(5) = 1; for j to N do cond[1][j] := f[j](0) = 0, (D(f[j]))(0) = 0, (D(f[j]))(5) = 0 end do; for i from 0 to N do dsolve({cond[1][i], equ[2][i]}, f[i](x)); assign(%) end do;```

```g := evalf@unapply(simplify(sum(f[n](x), n = 0 .. N)),x); convert(g(x), 'rational');   subs(x = 2.4, diff(g(x), x));```

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## You can use fsolve....

```convert(A,set): indets(%,name); fsolve(%%, % , (x->(x=0..1))~(%));```

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## Proc....

Try one of these :

```Button("Deduct", Evaluate(f = '[work(3), work(2)]')); Button("Deduct", Evaluate(f = 'proc() work(3);  work(2) end()'));```

## Op....

```2.55*10^(-90); op(%); %[1]/10^Digits; evalf(%,3);```

## Typos?...

Do You mean :

```N := 4; f:=unapply(sum(p^i*x, i = 0 .. N), x); HPMEq := (1-p)*(diff(f(x), x\$3))+p*(diff(f(x), x\$3)+(1/2)*(diff(f(x), x, x))*f(x));```

Edit:

```i := 'i': N := 4; F := sum(p^i*f[i](x), i = 0 .. N); HPMEq := (1 - p)*(diff(F, `\$`(x, 3))) + p*((diff(F, `\$`(x, 3))) + 1/2*(diff(F, x, x))*F); for i from 0 to N do equ[2][i] := coeff(HPMEq, p, i) = 0 end do;```

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## See ?mtaylor...

## I wonder what you meant......

Shouldn't this be like:

```MySolution:=proc(xl :: algebraic, is :: {float, integer}, x :: algebraic) if type(is, integer) then    return solve(xl=is,x); elif type(is, float) then    return solve(xl=is,x); end if; end proc; ```

## Some suggestions:...

See:

```?gfun,algeqtodiffeq with(gfun); algeqtodiffeq(y = y^4+y^2*z+1, y(z));```

also look at:
`?algcurves,algfun_series_sol`

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## Simple:...

```(diff(y(t), t))*(diff(y(t), t, t, t))-(diff(y(t), t))*y(t)^2-(diff(y(t), t))*(diff(y(t), t, t))-(diff(y(t), t))*A*y(t); map(int, %, t); student[intparts](%, diff(y(t), t)); (diff(y(t), t))*(diff(y(t), t, t))-(1/3)*y(t)^3-(1/2)*A*y(t)^2-(1/2)*(diff(y(t), t))^2+C+int((diff(y(s), s, s))^2, s = 0 .. t); %-%%; ```

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Where is the problem?

```a := 2: b := 10: c := -4: d := 5: rs := 4: A:={subs(filler=ln, filler(a*x+b)-filler(c*x+d) = rs)}; B:=map2(proc(x) x>0 end@op,1, indets(A, 'ln(dependent(x))')); solve(A union B); subs(%, A); evalf(indets(%,function));```

## Normal....

You can reason the use of normal, but factor always looks better.

```A:=((x^3+a*x+b) -(y^3+a*y+b) )^2/(x-y)^4; factor(A), normal(A); [(factor@numer, factor@denom)(A)], [(normal@numer, normal@denom)(A)]; G:=gcd((numer,denom)(A)); [factor(numer(A)/G), factor(denom(A)/G)], [normal(numer(A)/G), normal(denom(A)/G)];```

## Try this:...

```F := proc(E, V::{list, set})
local T := 'exp(anything)';
factor(subsindets(E, T, expand));
`@`(proc(E, R) combine(E, power)*collect(combine(R, power), V, factor) end proc, selectremove)(type, %,  {T, T^anything});
subsindets(%, T, factor);
end proc;

S := {Y = (nu__p+1)*(nu__p-3), Z = (nu__p+1)^2};

subs(S , F(simplify(Ty4, S, [nu__p, Y, Z]), [Y, Z, exp, kappa, omega]));
```

gives:

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## What is that formula?...

Try:
`map(((x -> x) = expand)@cos ,[5*t, 6*t]);`

Edit:
You can use ?solve,identity like Carl Love pointed out, or you can try this brute force method:
```A := cos(t)^6+a*cos(t)^4*sin(t)^2+b*cos(t)^2*sin(t)^4+c*sin(t)^6 = cos(6*t); combine((lhs-rhs)(A)); solve({coeffs}(%, indets(%, dependent(t))));```

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