Internal problem ID [2992]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 9
Problem number: 244.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {2 \left (1-x \right ) y^{\prime }-4 x \sqrt {1-x}-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve(2*(1-x)*diff(y(x),x) = 4*x*sqrt(1-x)+y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2}}{\sqrt {1-x}}+\frac {c_{1}}{\sqrt {x -1}} \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 27
DSolve[2(1-x)y'[x]==4 x Sqrt[1-x]+y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2+\frac {c_1}{\sqrt {2}}}{\sqrt {1-x}} \\ \end{align*}