11.2 problem 293

Internal problem ID [3041]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 11
Problem number: 293.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {\left (1-x^{2}\right ) y^{\prime }-a -4 y x=0} \end {gather*}

Solution by Maple

Time used: 0.001 (sec). Leaf size: 29

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

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

Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 30

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

\begin{align*} y(x)\to \frac {-a x \left (x^2-3\right )+3 c_1}{3 \left (x^2-1\right )^2} \\ \end{align*}