29.32.9 problem 943

Internal problem ID [5521]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 32
Problem number : 943
Date solved : Monday, January 27, 2025 at 11:35:10 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} y {y^{\prime }}^{2}&={\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.076 (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 {y \left (x \right ) {\mathrm e}^{2 x}}}{3 \sqrt {y \left (x \right )}} &= 0 \\ \frac {2 y \left (x \right )^{2}+3 c_{1} \sqrt {y \left (x \right )}+3 \sqrt {y \left (x \right ) {\mathrm e}^{2 x}}}{3 \sqrt {y \left (x \right )}} &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 2.139 (sec). Leaf size: 47

DSolve[y[x] (D[y[x],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*}