ODE
\[ y(x) y'(x)^2=e^{2 x} \] ODE Classification
[[_1st_order, _with_linear_symmetries]]
Book solution method
Change of variable
Mathematica ✓
cpu = 0.0145078 (sec), leaf count = 47
\[\left \{\left \{y(x)\to \left (\frac {3}{2}\right )^{2/3} \left (c_1-e^x\right ){}^{2/3}\right \},\left \{y(x)\to \left (\frac {3}{2}\right )^{2/3} \left (c_1+e^x\right ){}^{2/3}\right \}\right \}\]
Maple ✓
cpu = 0.076 (sec), leaf count = 50
\[ \left \{ -{1\sqrt {y \left ( x \right ) \left ( {{\rm e}^{x}} \right ) ^{2}}{\frac {1}{\sqrt {y \left ( x \right ) }}}}+{\frac {2}{3} \left ( y \left ( x \right ) \right ) ^{{\frac {3}{2}}}}+{\it \_C1}=0,{1\sqrt {y \left ( x \right ) \left ( {{\rm e}^{x}} \right ) ^{2}}{\frac {1}{\sqrt {y \left ( x \right ) }}}}+{\frac {2}{3} \left ( y \left ( x \right ) \right ) ^{{\frac {3}{2}}}}+{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[y[x]*y'[x]^2 == E^(2*x),y[x],x]
Mathematica raw output
{{y[x] -> (3/2)^(2/3)*(-E^x + C[1])^(2/3)}, {y[x] -> (3/2)^(2/3)*(E^x + C[1])^(2/3)}}
Maple raw input
dsolve(y(x)*diff(y(x),x)^2 = exp(2*x), y(x),'implicit')
Maple raw output
-1/y(x)^(1/2)*(y(x)*exp(x)^2)^(1/2)+2/3*y(x)^(3/2)+_C1 = 0, 1/y(x)^(1/2)*(y(x)*exp(x)^2)^(1/2)+2/3*y(x)^(3/2)+_C1 = 0