60.1.460 problem 463

Internal problem ID [10474]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 463
Date solved : Monday, January 27, 2025 at 07:54:41 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} y {y^{\prime }}^{2}-{\mathrm e}^{2 x}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.080 (sec). Leaf size: 67

dsolve(y(x)*diff(y(x),x)^2-exp(2*x) = 0,y(x), singsol=all)
 

\begin{align*} \frac {2 y^{2}+3 c_{1} \sqrt {y}-3 \sqrt {y \,{\mathrm e}^{2 x}}}{3 \sqrt {y}} &= 0 \\ \frac {2 y^{2}+3 c_{1} \sqrt {y}+3 \sqrt {y \,{\mathrm e}^{2 x}}}{3 \sqrt {y}} &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 2.111 (sec). Leaf size: 47

DSolve[-E^(2*x) + y[x]*D[y[x],x]^2==0,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*}