62.12.17 problem Ex 18

Internal problem ID [12863]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 19. Summary. Page 29
Problem number : Ex 18
Date solved : Tuesday, January 28, 2025 at 04:28:59 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (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: 0.062 (sec). Leaf size: 54

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

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