29.11.2 problem 293

Internal problem ID [4893]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 11
Problem number : 293
Date solved : Monday, January 27, 2025 at 09:46:44 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 30

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

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

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 30

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

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