29.9.14 problem 254

Internal problem ID [4854]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 9
Problem number : 254
Date solved : Monday, January 27, 2025 at 09:42:48 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 28

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

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