64.5.32 problem 35 (b)

Internal problem ID [13345]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 35 (b)
Date solved : Tuesday, January 28, 2025 at 05:31:15 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&=2 \sin \left (x \right )+5 \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 27

dsolve(diff(y(x),x)+y(x)=2*sin(x)+5*sin(2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.109 (sec). Leaf size: 37

DSolve[D[y[x],x]+y[x]==2*Sin[x]+5*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (\int _1^x2 e^{K[1]} (5 \cos (K[1])+1) \sin (K[1])dK[1]+c_1\right ) \]