69.1.1 problem 1

Internal problem ID [14154]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 06:16:14 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(diff(y(x),x)+y(x)*cos(x)=1/2*sin(2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.064 (sec). Leaf size: 54

DSolve[D[y[x],x]+y[x]*Cos[x]==1/2*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

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