Internal problem ID [3575]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 11
Problem number: 319.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x \left (a +x \right ) y^{\prime }-\left (b +c y\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.973 (sec). Leaf size: 65
DSolve[x(a+x)y'[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*}