ODE
\[ y'(x)^2=x^2+y(x) \] ODE Classification
[[_homogeneous, `class G`]]
Book solution method
Homogeneous ODE, The Isobaric equation
Mathematica ✗
cpu = 599.991 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 1.037 (sec), leaf count = 267
\[ \left \{ -\ln \left ( -{x}^{4}-{x}^{2}y \left ( x \right ) +4\, \left ( y \left ( x \right ) \right ) ^{2} \right ) -\ln \left ( -\sqrt {{x}^{2}+y \left ( x \right ) }x+2\,y \left ( x \right ) \right ) +\ln \left ( \sqrt {{x}^{2}+y \left ( x \right ) }x+2\,y \left ( x \right ) \right ) +{\frac {\sqrt {17}}{17} \left ( -2\,{\it Artanh} \left ( 1/17\,{\frac { \left ( x-4\,\sqrt {{x}^{2}+y \left ( x \right ) } \right ) \sqrt {17}}{x}} \right ) -2\,{\it Artanh} \left ( 1/17\,{\frac { \left ( {x}^{2}-8\,y \left ( x \right ) \right ) \sqrt {17}}{{x}^{2}}} \right ) +2\,{\it Artanh} \left ( 1/17\,{\frac { \left ( 4\,\sqrt {{x}^{2}+y \left ( x \right ) }+x \right ) \sqrt {17}}{x}} \right ) \right ) }-{\it \_C1}=0,\ln \left ( -{x}^{4}-{x}^{2}y \left ( x \right ) +4\, \left ( y \left ( x \right ) \right ) ^{2} \right ) -\ln \left ( -\sqrt {{x}^{2}+y \left ( x \right ) }x+2\,y \left ( x \right ) \right ) +\ln \left ( \sqrt {{x}^{2}+y \left ( x \right ) }x+2\,y \left ( x \right ) \right ) +{\frac {\sqrt {17}}{17} \left ( -2\,{\it Artanh} \left ( 1/17\,{\frac { \left ( x-4\,\sqrt {{x}^{2}+y \left ( x \right ) } \right ) \sqrt {17}}{x}} \right ) +2\,{\it Artanh} \left ( 1/17\,{\frac { \left ( {x}^{2}-8\,y \left ( x \right ) \right ) \sqrt {17}}{{x}^{2}}} \right ) +2\,{\it Artanh} \left ( 1/17\,{\frac { \left ( 4\,\sqrt {{x}^{2}+y \left ( x \right ) }+x \right ) \sqrt {17}}{x}} \right ) \right ) }-{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[y'[x]^2 == x^2 + y[x],y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(diff(y(x),x)^2 = x^2+y(x), y(x),'implicit')
Maple raw output
-ln(-x^4-x^2*y(x)+4*y(x)^2)-ln(-(x^2+y(x))^(1/2)*x+2*y(x))+ln((x^2+y(x))^(1/2)*x+2*y(x))+1/17*(-2*arctanh(1/17*(x-4*(x^2+y(x))^(1/2))*17^(1/2)/x)-2*arctanh(1/17*(x^2-8*y(x))*17^(1/2)/x^2)+2*arctanh(1/17*(4*(x^2+y(x))^(1/2)+x)*17^(1/2)/x))*17^(1/2)-_C1 = 0, ln(-x^4-x^2*y(x)+4*y(x)^2)-ln(-(x^2+y(x))^(1/2)*x+2*y(x))+ln((x^2+y(x))^(1/2)*x+2*y(x))+1/17*(-2*arctanh(1/17*(x-4*(x^2+y(x))^(1/2))*17^(1/2)/x)+2*arctanh(1/17*(x^2-8*y(x))*17^(1/2)/x^2)+2*arctanh(1/17*(4*(x^2+y(x))^(1/2)+x)*17^(1/2)/x))*17^(1/2)-_C1 = 0