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