Internal problem ID [14150]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {\left (-2+t \right ) y^{\prime }+\left (t^{2}-4\right ) y=\frac {1}{t +2}} \] With initial conditions \begin {align*} [y \left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 35
dsolve([(t-2)*diff(y(t),t)+(t^2-4)*y(t)=1/(t+2),y(0) = 3],y(t), singsol=all)
\[ y \left (t \right ) = \left (\int _{0}^{t}\frac {{\mathrm e}^{\frac {\textit {\_z1} \left (\textit {\_z1} +4\right )}{2}}}{\textit {\_z1}^{2}-4}d \textit {\_z1} +3\right ) {\mathrm e}^{-\frac {t \left (t +4\right )}{2}} \]
✓ Solution by Mathematica
Time used: 0.435 (sec). Leaf size: 46
DSolve[{(t-2)*y'[t]+(t^2-4)*y[t]==1/(t+2),{y[0]==3}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-\frac {1}{2} t (t+4)} \left (\int _0^t\frac {e^{\frac {1}{2} K[1] (K[1]+4)}}{K[1]^2-4}dK[1]+3\right ) \]