29.9.21 problem 261

Internal problem ID [4861]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 9
Problem number : 261
Date solved : Monday, January 27, 2025 at 09:43:17 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

Time used: 0.186 (sec). Leaf size: 36

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

\begin{align*} y(x)\to -\frac {(a-1) x^{a+1}}{b x^a-(a-1) c_1 x} \\ y(x)\to 0 \\ \end{align*}