4.17.40 \(x^2+4 x y'(x)+3 y'(x)^2-y(x)=0\)

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

\[ \left \{ {1 \left (\left (2\,{x}^{2}-2\,{\it \_C1}+8\,y \relax (x ) \right ) \sqrt {{x}^{2}+3\,y \relax (x ) }-x \left ({x}^{2}+{\it \_C1}+4\,y \relax (x ) \right ) \right ) \left (2\,\sqrt {{x}^{2}+3\,y \relax (x ) }+x \right ) ^{-1}}=0,2\,{\frac {\sqrt {{x}^{2}+3\,y \relax (x ) }}{ \left (2\,\sqrt {{x}^{2}+3\,y \relax (x ) }+x \right ) \left ({x}^{2}+4\,y \relax (x ) \right ) }}-{\frac {x}{{x}^{2}+4\,y \relax (x ) } \left (2\,\sqrt {{x}^{2}+3\,y \relax (x ) }+x \right ) ^{-1}}-{\it \_C1}=0,y \relax (x ) =-{\frac {{x}^{2}}{3}} \right \} \] 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