Internal problem ID [3062]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 11
Problem number: 314.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {x \left (1-x \right ) y^{\prime }+\left (1+2 x \right ) y-a=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 29
dsolve(x*(1-x)*diff(y(x),x)+(1+2*x)*y(x) = a,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (x^{3}-3 x^{2}+3 x -1\right ) c_{1}}{x}+\frac {a}{3 x} \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 23
DSolve[x(1-x)y'[x]+(1+2 x)y[x]==a,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {a-3 c_1 (x-1)^3}{3 x} \\ \end{align*}