Homework SourseVerify that the indicated function is a particular solution
Verify that the indicated function is a particular solution of the given differential equation. Give an interval of definition I for each solution.
y
y
Solution
y= x sin x + (cos x)ln(cos x) y\' = xcosx + sinx + (cos x)*(-sinx)/(cosx) - (sinx )ln(cos) =xcosx + sinx -sinx -(sinx )ln(cos) = xcosx - (sinx)ln(cosx) y\" = -x sinx + cosx + (sinx)*(sinx) /cosx - (cosx)ln(cosx) = -y +cosx + (sinx)*(sinx)/(cosx) y\"+y = ((cosx)*(cosx) + (sinx)*(sinx) )/cosx = sec x
