29.28.21 problem 819

Internal problem ID [5402]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 28
Problem number : 819
Date solved : Monday, January 27, 2025 at 11:20:53 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}+\left (a x +b y\right ) y^{\prime }+a b x y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

dsolve(diff(y(x),x)^2+(a*x+b*y(x))*diff(y(x),x)+a*b*x*y(x) = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -\frac {a \,x^{2}}{2}+c_{1} \\ y \left (x \right ) &= c_{1} {\mathrm e}^{-b x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 34

DSolve[(D[y[x],x])^2+(a*x+b*y[x])*D[y[x],x]+a*b*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 e^{-b x} \\ y(x)\to -\frac {a x^2}{2}+c_1 \\ y(x)\to 0 \\ \end{align*}