Internal problem ID [6512]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven
Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 7. Laplace Transforms. Section 7.5 Problesm for review and discovery. Section
A, Drill exercises. Page 309
Problem number: 4(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-7 y^{\prime }+12 y=t \,{\mathrm e}^{2 t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(t),t$2)-7*diff(y(t),t)+12*y(t)=t*exp(2*t),y(t), singsol=all)
\[ y \left (t \right ) = c_{2} {\mathrm e}^{3 t}+{\mathrm e}^{4 t} c_{1} +\frac {\left (2 t +3\right ) {\mathrm e}^{2 t}}{4} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 35
DSolve[y''[t]-7*y'[t]+12*y[t]==t*Exp[2*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{4} e^{2 t} \left (2 t+4 c_1 e^t+4 c_2 e^{2 t}+3\right ) \]