Internal problem ID [692]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, section 3.6, Variation of Parameters. page
190
Problem number: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }+y-\frac {{\mathrm e}^{t}}{t^{2}+1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.011 (sec). Leaf size: 30
dsolve(diff(y(t),t$2)-2*diff(y(t),t)+y(t) = exp(t)/(1+t^2),y(t), singsol=all)
\[ y \relax (t ) = c_{2} {\mathrm e}^{t}+t \,{\mathrm e}^{t} c_{1}-\frac {{\mathrm e}^{t} \left (-2 t \arctan \relax (t )+\ln \left (t^{2}+1\right )\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 33
DSolve[y''[t]-2*y'[t]+y[t] == Exp[t]/(1+t^2),y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{2} e^t \left (-\log \left (t^2+1\right )+2 (t (\text {ArcTan}(t)+c_2)+c_1)\right ) \\ \end{align*}