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 = 15.4326 (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 = 0.538 (sec), leaf count = 109
\[ \left \{ {\frac {1}{x} \left ( -{\it \_C2}\,x+\int ^{{\frac {y \left ( x \right ) }{x}}}\!{\frac {1}{{\it \_C1}\,{{\it \_f}}^{2}+{a}^{2}+{\it \_C1}}\sqrt { \left ( {{\it \_f}}^{2}+1 \right ) \left ( {\it \_C1}\,{{\it \_f}}^{2}+{a}^{2}+{\it \_C1} \right ) }}{d{\it \_f}}x-1 \right ) }=0,{\frac {1}{x} \left ( -{\it \_C2}\,x+\int ^{{\frac {y \left ( x \right ) }{x}}}\!{\frac {1}{{\it \_C1}\,{{\it \_f}}^{2}+{a}^{2}+{\it \_C1}}\sqrt { \left ( {{\it \_f}}^{2}+1 \right ) \left ( {\it \_C1}\,{{\it \_f}}^{2}+{a}^{2}+{\it \_C1} \right ) }}{d{\it \_f}}x+1 \right ) }=0 \right \} \] 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),'implicit')
Maple raw output
(-_C2*x+Intat(1/(_C1*_f^2+a^2+_C1)*((_f^2+1)*(_C1*_f^2+a^2+_C1))^(1/2),_f = y(x)/x)*x+1)/x = 0, (-_C2*x+Intat(1/(_C1*_f^2+a^2+_C1)*((_f^2+1)*(_C1*_f^2+a^2+_C1))^(1/2),_f = y(x)/x)*x-1)/x = 0