Internal problem ID [3282]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 19
Problem number: 538.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x +a \right ) \left (x +b \right ) y^{\prime }-y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 33
dsolve((a+x)*(b+x)*diff(y(x),x) = x*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (a +x \right )^{\frac {a}{a -b}} \left (b +x \right )^{-\frac {b}{a -b}} \]
✓ Solution by Mathematica
Time used: 0.132 (sec). Leaf size: 37
DSolve[(a+x)(b+x)y'[x]==x y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{\frac {a \log (a+x)-b \log (b+x)}{a-b}} \\ y(x)\to 0 \\ \end{align*}