81.3.6 problem 6

Internal problem ID [18624]
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 : 6
Date solved : Tuesday, January 28, 2025 at 12:04:33 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 21

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

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