35.3.11 problem 11

Internal problem ID [6115]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 3. Linear First-Order Equations. page 403
Problem number : 11
Date solved : Monday, January 27, 2025 at 01:36:26 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

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

\[ y = 2 \sin \left (x \right )-2+{\mathrm e}^{-\sin \left (x \right )} c_1 \]

✓ Solution by Mathematica

Time used: 0.081 (sec). Leaf size: 20

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

\[ y(x)\to 2 \sin (x)+c_1 e^{-\sin (x)}-2 \]