Internal problem ID [10772]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {x^{\prime }-x-\sin \left (t \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(x(t),t)=x(t)+sin(t),x(t), singsol=all)
\[ x \left (t \right ) = c_{1} {\mathrm e}^{t}-\frac {\cos \left (t \right )}{2}-\frac {\sin \left (t \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 24
DSolve[x'[t]==x[t]+Sin[t],x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -\frac {\sin (t)}{2}-\frac {\cos (t)}{2}+c_1 e^t \\ \end{align*}