Internal problem ID [4608]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 24. First order differential equations. Further problems 24. page 1068
Problem number: 31.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-y \tan \left (x \right )-\cos \left (x \right )+2 \sin \left (x \right ) x=0} \] With initial conditions \begin {align*} \left [y \left (\frac {\pi }{6}\right ) = 0\right ] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 22
dsolve([diff(y(x),x)-y(x)*tan(x)=cos(x)-2*x*sin(x),y(1/6*Pi) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (4 x \cos \left (2 x \right )-\pi +4 x \right ) \sec \left (x \right )}{8} \]
✓ Solution by Mathematica
Time used: 0.073 (sec). Leaf size: 17
DSolve[{y'[x]-y[x]*Tan[x]==Cos[x]-2*x*Sin[x],{y[Pi/6]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \cos (x)-\frac {1}{8} \pi \sec (x) \\ \end{align*}