29.11.24 problem 315

Internal problem ID [4915]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 11
Problem number : 315
Date solved : Monday, January 27, 2025 at 09:50:29 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 25

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

\[ y \left (x \right ) = \frac {12 c_{1} x^{4}+4 a x -3 a}{12 \left (x -1\right )^{2}} \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 29

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

\[ y(x)\to \frac {a (4 x-3)+12 c_1 x^4}{12 (x-1)^2} \]