Internal problem ID [3058]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 11
Problem number: 310.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {x \left (1-x \right ) y^{\prime }-a -\left (x +1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve(x*(1-x)*diff(y(x),x) = a+(1+x)*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (-a \ln \relax (x )-\frac {a}{x}+c_{1}\right ) x}{\left (x -1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 24
DSolve[x(1-x)y'[x]==a+(1+x)y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {a x \log (x)+a-c_1 x}{(x-1)^2} \\ \end{align*}