4.16.5 \(y'(x)^2=x^2+y(x)\)

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

\[ \left \{ -\ln \left (-{x}^{4}-{x}^{2}y \relax (x ) +4\, \left (y \relax (x ) \right ) ^{2} \right ) -\ln \left (-\sqrt {{x}^{2}+y \relax (x ) }x+2\,y \relax (x ) \right ) +\ln \left (\sqrt {{x}^{2}+y \relax (x ) }x+2\,y \relax (x ) \right ) +{\frac {\sqrt {17}}{17} \left (-2\,{\it Artanh} \left (1/17\,{\frac { \left (x-4\,\sqrt {{x}^{2}+y \relax (x ) } \right ) \sqrt {17}}{x}} \right ) -2\,{\it Artanh} \left (1/17\,{\frac { \left ({x}^{2}-8\,y \relax (x ) \right ) \sqrt {17}}{{x}^{2}}} \right ) +2\,{\it Artanh} \left (1/17\,{\frac { \left (4\,\sqrt {{x}^{2}+y \relax (x ) }+x \right ) \sqrt {17}}{x}} \right ) \right ) }-{\it \_C1}=0,\ln \left (-{x}^{4}-{x}^{2}y \relax (x ) +4\, \left (y \relax (x ) \right ) ^{2} \right ) -\ln \left (-\sqrt {{x}^{2}+y \relax (x ) }x+2\,y \relax (x ) \right ) +\ln \left (\sqrt {{x}^{2}+y \relax (x ) }x+2\,y \relax (x ) \right ) +{\frac {\sqrt {17}}{17} \left (-2\,{\it Artanh} \left (1/17\,{\frac { \left (x-4\,\sqrt {{x}^{2}+y \relax (x ) } \right ) \sqrt {17}}{x}} \right ) +2\,{\it Artanh} \left (1/17\,{\frac { \left ({x}^{2}-8\,y \relax (x ) \right ) \sqrt {17}}{{x}^{2}}} \right ) +2\,{\it Artanh} \left (1/17\,{\frac { \left (4\,\sqrt {{x}^{2}+y \relax (x ) }+x \right ) \sqrt {17}}{x}} \right ) \right ) }-{\it \_C1}=0 \right \} \] 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))*1
7^(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