29.6.13 problem 159

Internal problem ID [4759]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 6
Problem number : 159
Date solved : Monday, January 27, 2025 at 09:36:36 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

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

\[ y \left (x \right ) = c_{1} {\mathrm e}^{-b x} x^{-a} \]

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 28

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

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