26.22 problem 758

Internal problem ID [3491]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 26
Problem number: 758.
ODE order: 1.
ODE degree: 2.

CAS Maple gives this as type [_quadrature]

Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-a^{2} y^{2}=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 20

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

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

Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 31

DSolve[(y'[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*}