Internal problem ID [3063]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 11
Problem number: 315.
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 -2 \left (2-x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 29
dsolve(x*(1-x)*diff(y(x),x) = a+2*(2-x)*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (-a \left (\frac {1}{4 x^{4}}-\frac {1}{3 x^{3}}\right )+c_{1}\right ) x^{4}}{\left (x -1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 29
DSolve[x(1-x)y'[x]==a+2(2-x)y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {a (4 x-3)+12 c_1 x^4}{12 (x-1)^2} \\ \end{align*}