81.3.8 problem 8

Internal problem ID [18626]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter III. Ordinary differential equations of the first order and first degree. Exercises at page 33
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 12:04:37 PM
CAS classification : [_linear]

\begin{align*} x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=a \,x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 20

dsolve(x*(1-x^2)*diff(y(x),x)+(2*x^2-1)*y(x)=a*x^3,y(x), singsol=all)
 

\[ y \left (x \right ) = x \left (\sqrt {x -1}\, \sqrt {x +1}\, c_{1} +a \right ) \]

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 23

DSolve[x*(1-x^2)*D[y[x],x]+(2*x^2-1)*y[x]==a*x^3,y[x],x,IncludeSingularSolutions -> True]
 

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