Internal problem ID [14933]
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: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{\prime \prime }+x={\mathrm e}^{t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(x(t),t$2)+x(t)=exp(t),x(t), singsol=all)
\[ x \left (t \right ) = \sin \left (t \right ) c_{2} +\cos \left (t \right ) c_{1} +\frac {{\mathrm e}^{t}}{2} \]
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 23
DSolve[x''[t]+x[t]==Exp[t],x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {e^t}{2}+c_1 \cos (t)+c_2 \sin (t) \]