81.3.1 problem 1

Internal problem ID [18619]
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 : 1
Date solved : Tuesday, January 28, 2025 at 12:04:20 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {y}{x}&=-x^{2}+1 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 24

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

\[ y(x)\to -\frac {x^3}{4}+\frac {x}{2}+\frac {c_1}{x} \]