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]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=\frac {{\mathrm e}^{t}}{t^{2}+1}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 24
dsolve(diff(y(t),t$2)-2*diff(y(t),t)+y(t) = exp(t)/(1+t^2),y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{t} \left (c_{2} +c_{1} t -\frac {\ln \left (t^{2}+1\right )}{2}+t \arctan \left (t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 35
DSolve[y''[t]-2*y'[t]+y[t] == Exp[t]/(1+t^2),y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} e^t \left (2 t \arctan (t)-\log \left (t^2+1\right )+2 (c_2 t+c_1)\right ) \]