73.7.41 problem 41

Internal problem ID [15199]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 41
Date solved : Tuesday, January 28, 2025 at 07:41:53 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+2 y&=\sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 19

dsolve(diff(y(x),x)+2*y(x)=sin(x),y(x), singsol=all)
 

\[ y = -\frac {\cos \left (x \right )}{5}+\frac {2 \sin \left (x \right )}{5}+c_{1} {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 31

DSolve[D[y[x],x]+2*y[x]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (\int _1^xe^{2 K[1]} \sin (K[1])dK[1]+c_1\right ) \]