ODE
\[ a^2 y(x)+\left (x^2+y(x)^2\right )^2 y''(x)=0 \] ODE Classification
[NONE]
Book solution method
TO DO
Mathematica ✗
cpu = 31.6764 (sec), leaf count = 0 , could not solve
DSolve[a^2*y[x] + (x^2 + y[x]^2)^2*Derivative[2][y][x] == 0, y[x], x]
Maple ✓
cpu = 1.256 (sec), leaf count = 112
\[\left [y \left (x \right ) = \RootOf \left (\left (\int _{}^{\textit {\_Z}}\frac {\sqrt {\textit {\_C1} \,\textit {\_f}^{4}+\textit {\_f}^{2} a^{2}+2 \textit {\_C1} \,\textit {\_f}^{2}+a^{2}+\textit {\_C1}}}{\textit {\_C1} \,\textit {\_f}^{2}+a^{2}+\textit {\_C1}}d \textit {\_f} \right ) x +\textit {\_C2} x +1\right ) x, y \left (x \right ) = \RootOf \left (-\left (\int _{}^{\textit {\_Z}}\frac {\sqrt {\textit {\_C1} \,\textit {\_f}^{4}+\textit {\_f}^{2} a^{2}+2 \textit {\_C1} \,\textit {\_f}^{2}+a^{2}+\textit {\_C1}}}{\textit {\_C1} \,\textit {\_f}^{2}+a^{2}+\textit {\_C1}}d \textit {\_f} \right ) x +\textit {\_C2} x +1\right ) x\right ]\] Mathematica raw input
DSolve[a^2*y[x] + (x^2 + y[x]^2)^2*y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[a^2*y[x] + (x^2 + y[x]^2)^2*Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve((x^2+y(x)^2)^2*diff(diff(y(x),x),x)+a^2*y(x) = 0, y(x))
Maple raw output
[y(x) = RootOf(Intat(1/(_C1*_f^2+a^2+_C1)*(_C1*_f^4+_f^2*a^2+2*_C1*_f^2+a^2+_C1)^(1/2),_f = _Z)*x+_C2*x+1)*x, y(x) = RootOf(-Intat(1/(_C1*_f^2+a^2+_C1)*(_C1*_f^4+_f^2*a^2+2*_C1*_f^2+a^2+_C1)^(1/2),_f = _Z)*x+_C2*x+1)*x]