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

ODE
$$4y^{\prime }(x{)}^2+2e^{2x-2y(x)}{y}^{\prime }(x)-e^{2x-2y(x)}=0$$ 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

$$\{x+{\mathrm{e}}^{2y\left(x\right)-2x}\sqrt{(4{\mathrm{e}}^{2y\left(x\right)-2x}+1){\mathrm{e}}^{-4y\left(x\right)+4x}}\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\frac{1}{\sqrt{4{\mathrm{e}}^{2y\left(x\right)-2x}+1}}\right)\frac{1}{\sqrt{4{\mathrm{e}}^{2y\left(x\right)-2x}+1}}+\ln \left({\mathrm{e}}^{y\left(x\right)-x}\right)-\mathit{\_}\mathit{C}\mathit{1}=0,x+\ln \left({\mathrm{e}}^{y\left(x\right)-x}\right)-{\mathrm{e}}^{2y\left(x\right)-2x}\sqrt{(4{\mathrm{e}}^{2y\left(x\right)-2x}+1){\mathrm{e}}^{-4y\left(x\right)+4x}}\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\frac{1}{\sqrt{4{\mathrm{e}}^{2y\left(x\right)-2x}+1}}\right)\frac{1}{\sqrt{4{\mathrm{e}}^{2y\left(x\right)-2x}+1}}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$ 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