Internal problem ID [14853]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 32.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y^{\prime }+20 y=-2 t \,{\mathrm e}^{t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(t),t$2)+9*diff(y(t),t)+20*y(t)=-2*t*exp(t),y(t), singsol=all)
\[ y \left (t \right ) = -\frac {{\mathrm e}^{-5 t} \left (\left (t -\frac {11}{30}\right ) {\mathrm e}^{6 t}-15 \,{\mathrm e}^{t} c_{1} -15 c_{2} \right )}{15} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 34
DSolve[y''[t]+9*y'[t]+20*y[t]==-2*t*Exp[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{450} e^t (11-30 t)+c_1 e^{-5 t}+c_2 e^{-4 t} \]