ODE
\[ x^2+4 x y'(x)+3 y'(x)^2-y(x)=0 \] ODE Classification
[[_homogeneous, `class G`]]
Book solution method
Change of variable
Mathematica ✗
cpu = 600.006 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.125 (sec), leaf count = 138
\[ \left \{ {1 \left ( \left ( 2\,{x}^{2}-2\,{\it \_C1}+8\,y \left ( x \right ) \right ) \sqrt {{x}^{2}+3\,y \left ( x \right ) }-x \left ( {x}^{2}+{\it \_C1}+4\,y \left ( x \right ) \right ) \right ) \left ( 2\,\sqrt {{x}^{2}+3\,y \left ( x \right ) }+x \right ) ^{-1}}=0,2\,{\frac {\sqrt {{x}^{2}+3\,y \left ( x \right ) }}{ \left ( 2\,\sqrt {{x}^{2}+3\,y \left ( x \right ) }+x \right ) \left ( {x}^{2}+4\,y \left ( x \right ) \right ) }}-{\frac {x}{{x}^{2}+4\,y \left ( x \right ) } \left ( 2\,\sqrt {{x}^{2}+3\,y \left ( x \right ) }+x \right ) ^{-1}}-{\it \_C1}=0,y \left ( x \right ) =-{\frac {{x}^{2}}{3}} \right \} \] Mathematica raw input
DSolve[x^2 - y[x] + 4*x*y'[x] + 3*y'[x]^2 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(3*diff(y(x),x)^2+4*x*diff(y(x),x)+x^2-y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = -1/3*x^2, 2/(2*(x^2+3*y(x))^(1/2)+x)/(x^2+4*y(x))*(x^2+3*y(x))^(1/2)-1/(2*(x^2+3*y(x))^(1/2)+x)/(x^2+4*y(x))*x-_C1 = 0, ((2*x^2-2*_C1+8*y(x))*(x^2+3*y(x))^(1/2)-x*(x^2+_C1+4*y(x)))/(2*(x^2+3*y(x))^(1/2)+x) = 0