Internal problem ID [10434]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY.
2015.
Section: Chapter 2, Second order linear equations. Section 2.3.1 Nonhomogeneous Equations:
Undetermined Coefficients. Exercises page 110
Problem number: 1(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime }+x^{\prime }+x-3 t^{3}+1=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(diff(x(t),t$2)+diff(x(t),t)+x(t)=3*t^3-1,x(t), singsol=all)
\[ x \left (t \right ) = {\mathrm e}^{-\frac {t}{2}} \sin \left (\frac {\sqrt {3}\, t}{2}\right ) c_{2} +{\mathrm e}^{-\frac {t}{2}} \cos \left (\frac {\sqrt {3}\, t}{2}\right ) c_{1} +3 t^{3}-9 t^{2}+17 \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 52
DSolve[x''[t]+x'[t]+x[t]==3*t^3-1,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 3 (t-3) t^2+e^{-t/2} \left (c_2 \cos \left (\frac {\sqrt {3} t}{2}\right )+c_1 \sin \left (\frac {\sqrt {3} t}{2}\right )\right )+17 \\ \end{align*}