4.19.47 $y(x)y^{\prime }(x{)}^2=e^{2x}$

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

[[_1st_order, _with_linear_symmetries]]

Book solution method
Change of variable

Mathematica ✓
cpu = 0.0145078 (sec), leaf count = 47

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

Maple ✓
cpu = 0.076 (sec), leaf count = 50

$$\{-1\sqrt{y\left(x\right){\left({\mathrm{e}}^x\right)}^2}\frac{1}{\sqrt{y\left(x\right)}}+\frac{2}{3}{\left(y\left(x\right)\right)}^{\frac{3}{2}}+\mathit{\_}\mathit{C}\mathit{1}=0,1\sqrt{y\left(x\right){\left({\mathrm{e}}^x\right)}^2}\frac{1}{\sqrt{y\left(x\right)}}+\frac{2}{3}{\left(y\left(x\right)\right)}^{\frac{3}{2}}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$ 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)*e
xp(x)^2)^(1/2)+2/3*y(x)^(3/2)+_C1 = 0