Internal problem ID [14932]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 6. Systems of Differential Equations. Exercises 6.1, page 282
Problem number: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime }+16 x=\sin \left (t \right ) t} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(x(t),t$2)+16*x(t)=t*sin(t),x(t), singsol=all)
\[ x \left (t \right ) = c_{2} \sin \left (4 t \right )+c_{1} \cos \left (4 t \right )-\frac {2 \cos \left (t \right )}{225}+\frac {\sin \left (t \right ) t}{15} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 33
DSolve[x''[t]+16*x[t]==t*Sin[t],x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{15} t \sin (t)-\frac {2 \cos (t)}{225}+c_1 \cos (4 t)+c_2 \sin (4 t) \]