12.2.19 problem 19

Internal problem ID [1555]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number : 19
Date solved : Monday, January 27, 2025 at 04:59:56 AM
CAS classification : [_linear]

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

✓ Solution by Maple

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

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

\[ y = \frac {\frac {x^{2}}{2}+2 \ln \left (x \right )+c_1}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 22

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

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