29.9.20 problem 260

Internal problem ID [4860]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 9
Problem number : 260
Date solved : Monday, January 27, 2025 at 09:43:02 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

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

\[ y \left (x \right ) = -\frac {x}{a \ln \left (x \right )-c_{1}} \]

✓ Solution by Mathematica

Time used: 0.161 (sec). Leaf size: 22

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

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