Internal problem ID [1756]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.4, The method of variation of parameters. Page 154
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {2 y^{\prime \prime }-3 y^{\prime }+y=\left (t^{2}+1\right ) {\mathrm e}^{t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(2*diff(y(t),t$2)-3*diff(y(t),t)+y(t)=(t^2+1)*exp(t),y(t), singsol=all)
\[ y \left (t \right ) = c_{2} {\mathrm e}^{\frac {t}{2}}+\frac {{\mathrm e}^{t} \left (t^{3}-6 t^{2}+6 c_{1} +27 t -54\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.071 (sec). Leaf size: 39
DSolve[2*y''[t]-3*y'[t]+y[t]==(t^2+1)*Exp[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^t \left (\frac {t^3}{3}-2 t^2+9 t-18+c_2\right )+c_1 e^{t/2} \]