29.11.28 problem 319

Internal problem ID [4919]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 11
Problem number : 319
Date solved : Monday, January 27, 2025 at 09:50:36 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 32

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

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

✓ Solution by Mathematica

Time used: 1.063 (sec). Leaf size: 65

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

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