Internal problem ID [10456]
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: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime }+2 x-\cos \left (\sqrt {2}\, t \right )=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve([diff(x(t),t$2)+2*x(t)=cos(sqrt(2)*t),x(0) = 0, D(x)(0) = 1],x(t), singsol=all)
\[ x \left (t \right ) = \frac {\sin \left (\sqrt {2}\, t \right ) \sqrt {2}\, \left (t +2\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.078 (sec). Leaf size: 25
DSolve[{x''[t]+2*x[t]==Cos[Sqrt[2]*t],{x[0]==0,x'[0]==1}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {(t+2) \sin \left (\sqrt {2} t\right )}{2 \sqrt {2}} \\ \end{align*}