67.2.45 problem Problem 18(j)

Internal problem ID [14002]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 18(j)
Date solved : Tuesday, January 28, 2025 at 06:11:26 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 5.257 (sec). Leaf size: 62

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

\[ y(x)\to \exp \left (\int _1^x-\sin (K[2])dK[2]\right ) \left (\int _1^x\exp \left (-\int _1^{K[3]}-\sin (K[2])dK[2]\right ) \left (c_1+\int _1^{K[3]}\cos (K[1])dK[1]\right )dK[3]+c_2\right ) \]