Internal problem ID [1648]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.2. Page 6
Problem number: Example 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+y=\frac {1}{t^{2}+1}} \] With initial conditions \begin {align*} [y \left (2\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.828 (sec). Leaf size: 65
dsolve([diff(y(t),t)+y(t)=1/(1+t^2),y(2) = 3],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (i {\mathrm e}^{i} \operatorname {Ei}_{1}\left (-t +i\right )-i {\mathrm e}^{-i} \operatorname {Ei}_{1}\left (-t -i\right )-i {\mathrm e}^{i} \operatorname {Ei}_{1}\left (-2+i\right )+i {\mathrm e}^{-i} \operatorname {Ei}_{1}\left (-2-i\right )+6 \,{\mathrm e}^{2}\right ) {\mathrm e}^{-t}}{2} \]
✓ Solution by Mathematica
Time used: 0.124 (sec). Leaf size: 72
DSolve[{y'[t]+y[t]==1/(1+t^2),y[1]==2},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} e^{-t-i} \left (-i e^{2 i} \operatorname {ExpIntegralEi}(t-i)+i \operatorname {ExpIntegralEi}(t+i)-i \operatorname {ExpIntegralEi}(1+i)+i e^{2 i} \operatorname {ExpIntegralEi}(1-i)+4 e^{1+i}\right ) \]