##### 4.19.47 $$y(x) y'(x)^2=e^{2 x}$$

ODE
$y(x) y'(x)^2=e^{2 x}$ ODE Classiﬁcation

[[_1st_order, _with_linear_symmetries]]

Book solution method
Change of variable

Mathematica
cpu = 0.198203 (sec), leaf count = 47

$\left \{\left \{y(x)\to \left (\frac {3}{2}\right )^{2/3} \left (-e^x+c_1\right ){}^{2/3}\right \},\left \{y(x)\to \left (\frac {3}{2}\right )^{2/3} \left (e^x+c_1\right ){}^{2/3}\right \}\right \}$

Maple
cpu = 0.36 (sec), leaf count = 50

$\left [-\frac {\sqrt {{\mathrm e}^{2 x} y \left (x \right )}}{\sqrt {y \left (x \right )}}+\frac {2 y \left (x \right )^{\frac {3}{2}}}{3}+\textit {\_C1} = 0, \frac {\sqrt {{\mathrm e}^{2 x} y \left (x \right )}}{\sqrt {y \left (x \right )}}+\frac {2 y \left (x \right )^{\frac {3}{2}}}{3}+\textit {\_C1} = 0\right ]$ 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))

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]