Internal problem ID [4177]
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]]
\[ \boxed {y {y^{\prime }}^{2}={\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 67
dsolve(y(x)*diff(y(x),x)^2 = exp(2*x),y(x), singsol=all)
\begin{align*} \frac {2 y \left (x \right )^{2}+3 c_{1} \sqrt {y \left (x \right )}-3 \sqrt {{\mathrm e}^{2 x} y \left (x \right )}}{3 \sqrt {y \left (x \right )}} &= 0 \\ \frac {2 y \left (x \right )^{2}+3 c_{1} \sqrt {y \left (x \right )}+3 \sqrt {{\mathrm e}^{2 x} y \left (x \right )}}{3 \sqrt {y \left (x \right )}} &= 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.162 (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*}