Internal problem ID [4660]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. page
95
Problem number: Problem 11.6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-6 y^{\prime }+25 y-50 t^{3}+36 t^{2}+63 t -18=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 33
dsolve(diff(y(t),t$2)-6*diff(y(t),t)+25*y(t)=50*t^3-36*t^2-63*t+18,y(t), singsol=all)
\[ y \relax (t ) = {\mathrm e}^{3 t} \sin \left (4 t \right ) c_{2}+{\mathrm e}^{3 t} \cos \left (4 t \right ) c_{1}+2 t^{3}-3 t \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 36
DSolve[y''[t]-6*y'[t]+25*y[t]==50*t^3-36*t^2-63*t+18,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to t \left (2 t^2-3\right )+e^{3 t} (c_2 \cos (4 t)+c_1 \sin (4 t)) \\ \end{align*}