4.17.34 \(y'(x)^2=e^{4 x-2 y(x)} \left (y'(x)-1\right )\)

ODE
\[ y'(x)^2=e^{4 x-2 y(x)} \left (y'(x)-1\right ) \] ODE Classification

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

Book solution method
Change of variable

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

$Failed

Maple
cpu = 0.372 (sec), leaf count = 259

\[ \left \{ x-{\frac {{{\rm e}^{2\,y \relax (x ) -4\,x}}}{2}\sqrt {- \left (4\,{{\rm e}^{2\,y \relax (x ) -4\,x}}-1 \right ) {{\rm e}^{8\,x-4\,y \relax (x ) }}}{\it Artanh} \left ({\frac {1}{\sqrt {-4\,{{\rm e}^{2\,y \relax (x ) -4\,x}}+1}}} \right ) {\frac {1}{\sqrt {-4\,{{\rm e}^{2\,y \relax (x ) -4\,x}}+1}}}}-{\frac {\ln \left (2\,{{\rm e}^{y \relax (x ) -2\,x}}-1 \right ) }{4}}+{\frac {\ln \left ({{\rm e}^{y \relax (x ) -2\,x}} \right ) }{2}}-{\frac {\ln \left (1+2\,{{\rm e}^{y \relax (x ) -2\,x}} \right ) }{4}}+{\frac {\ln \left (4\,{{\rm e}^{2\,y \relax (x ) -4\,x}}-1 \right ) }{4}}-{\it \_C1}=0,x+{\frac {\ln \left (4\,{{\rm e}^{2\,y \relax (x ) -4\,x}}-1 \right ) }{4}}-{\frac {\ln \left (2\,{{\rm e}^{y \relax (x ) -2\,x}}-1 \right ) }{4}}+{\frac {\ln \left ({{\rm e}^{y \relax (x ) -2\,x}} \right ) }{2}}-{\frac {\ln \left (1+2\,{{\rm e}^{y \relax (x ) -2\,x}} \right ) }{4}}+{\frac {{{\rm e}^{2\,y \relax (x ) -4\,x}}}{2}\sqrt {- \left (4\,{{\rm e}^{2\,y \relax (x ) -4\,x}}-1 \right ) {{\rm e}^{8\,x-4\,y \relax (x ) }}}{\it Artanh} \left ({\frac {1}{\sqrt {-4\,{{\rm e}^{2\,y \relax (x ) -4\,x}}+1}}} \right ) {\frac {1}{\sqrt {-4\,{{\rm e}^{2\,y \relax (x ) -4\,x}}+1}}}}-{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[y'[x]^2 == E^(4*x - 2*y[x])*(-1 + y'[x]),y[x],x]

Mathematica raw output

{}

Maple raw input

dsolve(diff(y(x),x)^2 = exp(4*x-2*y(x))*(diff(y(x),x)-1), y(x),'implicit')

Maple raw output

x-1/2*(-(4*exp(2*y(x)-4*x)-1)*exp(8*x-4*y(x)))^(1/2)*exp(2*y(x)-4*x)/(-4*exp(2*y
(x)-4*x)+1)^(1/2)*arctanh(1/(-4*exp(2*y(x)-4*x)+1)^(1/2))-1/4*ln(2*exp(y(x)-2*x)
-1)+1/2*ln(exp(y(x)-2*x))-1/4*ln(1+2*exp(y(x)-2*x))+1/4*ln(4*exp(2*y(x)-4*x)-1)-
_C1 = 0, x+1/4*ln(4*exp(2*y(x)-4*x)-1)-1/4*ln(2*exp(y(x)-2*x)-1)+1/2*ln(exp(y(x)
-2*x))-1/4*ln(1+2*exp(y(x)-2*x))+1/2*(-(4*exp(2*y(x)-4*x)-1)*exp(8*x-4*y(x)))^(1
/2)*exp(2*y(x)-4*x)/(-4*exp(2*y(x)-4*x)+1)^(1/2)*arctanh(1/(-4*exp(2*y(x)-4*x)+1
)^(1/2))-_C1 = 0