Internal problem ID [14546]
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: 40.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-7 y^{\prime }+12 y=-2 t^{3} {\mathrm e}^{4 t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(diff(y(t),t$2)-7*diff(y(t),t)+12*y(t)=-2*t^3*exp(4*t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (-t^{4}+4 t^{3}-12 t^{2}+2 c_{2} +24 t \right ) {\mathrm e}^{4 t}}{2}+c_{1} {\mathrm e}^{3 t} \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 42
DSolve[y''[t]-7*y'[t]+12*y[t]==-2*t^3*Exp[4*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{3 t} \left (e^t \left (-\frac {t^4}{2}+2 t^3-6 t^2+12 t-12+c_2\right )+c_1\right ) \]