12.2.35 problem 35

Internal problem ID [1571]
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 : 35
Date solved : Monday, January 27, 2025 at 05:00:43 AM
CAS classification : [_linear]

\begin{align*} \left (x +2\right ) y^{\prime }+4 y&=\frac {2 x^{2}+1}{x \left (x +2\right )^{3}} \end{align*}

With initial conditions

\begin{align*} y \left (-1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 20

dsolve([(x+2)*diff(y(x),x)+4*y(x)= (1+2*x^2)/(x*(x+2)^3),y(-1) = 2],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 23

DSolve[{(x+2)*D[y[x],x]+4*y[x]== (1+2*x^2)/(x*(x+2)^3),y[-1]==2},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^2+\log (x)-i \pi +1}{(x+2)^4} \]