\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( y \left ( x \right ) \right ) ^{2}+a{x}^{m}=0} \]
Mathematica: cpu = 0.010501 (sec), leaf count = 254\[ y(x)= -\frac {i \sqrt {-a} x^{\frac {m+2}{2}} \left (c_1 J_{\frac {m+1}{m+2}}(z)-c_1 J_{-\frac {m+3}{m+2}}(z)-2 J_{\frac {1}{m+2}-1}(z)\right )-c_1 J_{-\frac {1}{m+2}}(z)}{2 x \left (c_1 J_{-\frac {1}{m+2}}(z)+J_{\frac {1}{m+2}}(z)\right )} \] Where \[ z = \left (\frac {2 i \sqrt {-a} x^{\frac {m}{2}+1}}{m+2}\right ) \]
Maple: cpu = 0.093 (sec), leaf count = 189 \[ \left \{ y \left ( x \right ) =-{\frac {1}{x} \left ( \sqrt {a}{x}^{{ \frac {m}{2}}+1}{{\sl J}_{{\frac {3+m}{m+2}}}\left (2\,{\frac {\sqrt {a }{x}^{m/2+1}}{m+2}}\right )}{\it \_C1}+{{\sl Y}_{{\frac {3+m}{m+2}} }\left (2\,{\frac {\sqrt {a}{x}^{m/2+1}}{m+2}}\right )}\sqrt {a}{x}^{{ \frac {m}{2}}+1}-{\it \_C1}\,{{\sl J}_{ \left ( m+2 \right ) ^{-1} }\left (2\,{\frac {\sqrt {a}{x}^{m/2+1}}{m+2}}\right )}-{{\sl Y}_{ \left ( m+2 \right ) ^{-1}}\left (2\,{\frac {\sqrt {a}{x}^{m/2+1}}{m+2}} \right )} \right ) \left ( {\it \_C1}\,{{\sl J}_{ \left ( m+2 \right ) ^{- 1}}\left (2\,{\frac {\sqrt {a}{x}^{m/2+1}}{m+2}}\right )}+{{\sl Y}_{ \left ( m+2 \right ) ^{-1}}\left (2\,{\frac {\sqrt {a}{x}^{m/2+1}}{m+2}} \right )} \right ) ^{-1}} \right \} \]
Sage: cpu = 0 (sec), leaf count = 0 \[ \text {Maxima was unable to solve this ODE} \]