83.2.8 problem 8

Internal problem ID [19054]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (A) at page 8
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 12:49:29 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 29

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

\[ y(x)\to \frac {x^4-2 x^2+4 c_1}{4 \left (x^2-1\right )} \]