Internal problem ID [14056]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+y=\sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(x),x)+y(x)=sin(x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\cos \left (x \right )}{2}+\frac {\sin \left (x \right )}{2}+c_{1} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 25
DSolve[y'[x]+y[x]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \left (\sin (x)-\cos (x)+2 c_1 e^{-x}\right ) \]