29.11.23 problem 314

Internal problem ID [4914]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 11
Problem number : 314
Date solved : Monday, January 27, 2025 at 09:50:27 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 23

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

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