29.9.4 problem 244

Internal problem ID [4844]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 9
Problem number : 244
Date solved : Monday, January 27, 2025 at 09:42:27 AM
CAS classification : [_linear]

\begin{align*} 2 \left (1-x \right ) y^{\prime }&=4 x \sqrt {1-x}+y \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(2*(1-x)*diff(y(x),x) = 4*x*sqrt(1-x)+y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {x^{2}}{\sqrt {1-x}}+\frac {c_{1}}{\sqrt {x -1}} \]

✓ Solution by Mathematica

Time used: 0.063 (sec). Leaf size: 32

DSolve[2(1-x)D[y[x],x]==4 x Sqrt[1-x]+y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2 x^2+\sqrt {2} c_1}{2 \sqrt {1-x}} \]