Internal problem ID [3669]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 32
Problem number: 943.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y \left (y^{\prime }\right )^{2}-{\mathrm e}^{2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.219 (sec). Leaf size: 50
dsolve(y(x)*diff(y(x),x)^2 = exp(2*x),y(x), singsol=all)
\begin{align*} -\frac {\sqrt {y \relax (x ) {\mathrm e}^{2 x}}}{\sqrt {y \relax (x )}}+\frac {2 y \relax (x )^{\frac {3}{2}}}{3}+c_{1} = 0 \\ \frac {\sqrt {y \relax (x ) {\mathrm e}^{2 x}}}{\sqrt {y \relax (x )}}+\frac {2 y \relax (x )^{\frac {3}{2}}}{3}+c_{1} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.232 (sec). Leaf size: 47
DSolve[y[x] (y'[x])^2==Exp[2 x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (\frac {3}{2}\right )^{2/3} \left (-e^x+c_1\right ){}^{2/3} \\ y(x)\to \left (\frac {3}{2}\right )^{2/3} \left (e^x+c_1\right ){}^{2/3} \\ \end{align*}