Internal problem ID [14545]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number: 39.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }-5 y=-648 t^{2} {\mathrm e}^{5 t}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve(diff(y(t),t$2)-4*diff(y(t),t)-5*y(t)=-648*t^2*exp(5*t),y(t), singsol=all)
\[ y \left (t \right ) = \left (-36 t^{3}+18 t^{2}+c_{2} -6 t \right ) {\mathrm e}^{5 t}+{\mathrm e}^{-t} c_{1} \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 37
DSolve[y''[t]-4*y'[t]-5*y[t]==-648*t^2*Exp[5*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-t} \left (e^{6 t} \left (-36 t^3+18 t^2-6 t+1+c_2\right )+c_1\right ) \]