29.26.22 problem 758

Internal problem ID [5343]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 26
Problem number : 758
Date solved : Monday, January 27, 2025 at 11:15:56 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}&=a^{2} y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

dsolve(diff(y(x),x)^2 = a^2*y(x)^2,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= c_{1} {\mathrm e}^{a x} \\ y \left (x \right ) &= c_{1} {\mathrm e}^{-a x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 31

DSolve[(D[y[x],x])^2==a^2*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 e^{-a x} \\ y(x)\to c_1 e^{a x} \\ y(x)\to 0 \\ \end{align*}