Internal problem ID [921]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (2+x \right ) y^{\prime }+4 y-\frac {2 x^{2}+1}{x \left (2+x \right )^{3}}=0} \end {gather*} With initial conditions \begin {align*} [y \left (-1\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
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)
\[ y \relax (x ) = \frac {x^{2}+\ln \relax (x )+1-i \pi }{\left (2+x \right )^{4}} \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 23
DSolve[{(x+2)*y'[x]+4*y[x]== (1+2*x^2)/(x*(x+2)^3),y[-1]==2},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2+\log (x)-i \pi +1}{(x+2)^4} \\ \end{align*}