4.17.43 \(4 y'(x)^2+2 e^{2 x-2 y(x)} y'(x)-e^{2 x-2 y(x)}=0\)

ODE
\[ 4 y'(x)^2+2 e^{2 x-2 y(x)} y'(x)-e^{2 x-2 y(x)}=0 \] ODE Classification

[[_homogeneous, `class C`], _dAlembert]

Book solution method
Change of variable

Mathematica
cpu = 0 (sec), leaf count = 0 , $Failed

$Failed

Maple
cpu = 0.303 (sec), leaf count = 164

\[ \left \{ x+{{{\rm e}^{2\,y \relax (x ) -2\,x}}\sqrt { \left (4\,{{\rm e}^{2\,y \relax (x ) -2\,x}}+1 \right ) {{\rm e}^{-4\,y \relax (x ) +4\,x}}}{\it Artanh} \left ({\frac {1}{\sqrt {4\,{{\rm e}^{2\,y \relax (x ) -2\,x}}+1}}} \right ) {\frac {1}{\sqrt {4\,{{\rm e}^{2\,y \relax (x ) -2\,x}}+1}}}}+\ln \left ({{\rm e}^{y \relax (x ) -x}} \right ) -{\it \_C1}=0,x+\ln \left ({{\rm e}^{y \relax (x ) -x}} \right ) -{{{\rm e}^{2\,y \relax (x ) -2\,x}}\sqrt { \left (4\,{{\rm e}^{2\,y \relax (x ) -2\,x}}+1 \right ) {{\rm e}^{-4\,y \relax (x ) +4\,x}}}{\it Artanh} \left ({\frac {1}{\sqrt {4\,{{\rm e}^{2\,y \relax (x ) -2\,x}}+1}}} \right ) {\frac {1}{\sqrt {4\,{{\rm e}^{2\,y \relax (x ) -2\,x}}+1}}}}-{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[-E^(2*x - 2*y[x]) + 2*E^(2*x - 2*y[x])*y'[x] + 4*y'[x]^2 == 0,y[x],x]

Mathematica raw output

{}

Maple raw input

dsolve(4*diff(y(x),x)^2+2*exp(2*x-2*y(x))*diff(y(x),x)-exp(2*x-2*y(x)) = 0, y(x),'implicit')

Maple raw output

x+((4*exp(2*y(x)-2*x)+1)*exp(-4*y(x)+4*x))^(1/2)*exp(2*y(x)-2*x)/(4*exp(2*y(x)-2
*x)+1)^(1/2)*arctanh(1/(4*exp(2*y(x)-2*x)+1)^(1/2))+ln(exp(y(x)-x))-_C1 = 0, x+l
n(exp(y(x)-x))-((4*exp(2*y(x)-2*x)+1)*exp(-4*y(x)+4*x))^(1/2)*exp(2*y(x)-2*x)/(4
*exp(2*y(x)-2*x)+1)^(1/2)*arctanh(1/(4*exp(2*y(x)-2*x)+1)^(1/2))-_C1 = 0