2.45 problem Problem 18(j)

Internal problem ID [10918]

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).
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\[ \boxed {y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y \cos \left (x \right )-\cos \left (x \right )=0} \]

Solution by Maple

Time used: 0.016 (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)
 

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

Solution by Mathematica

Time used: 0.732 (sec). Leaf size: 34

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

\begin{align*} y(x)\to e^{\cos (x)} \left (\int _1^xe^{-\cos (K[1])} (c_1+\sin (K[1]))dK[1]+c_2\right ) \\ \end{align*}