29.20.15 problem 560

Internal problem ID [5156]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 20
Problem number : 560
Date solved : Monday, January 27, 2025 at 10:16:21 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.051 (sec). Leaf size: 44

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

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

✓ Solution by Mathematica

Time used: 0.869 (sec). Leaf size: 36

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

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