2.31 problem 31

Internal problem ID [4609]

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]

Solve \begin {gather*} \boxed {y^{\prime }-y \tan \relax (x )-\cos \relax (x )+2 x \sin \relax (x )=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {\pi }{6}\right ) = 0\right ] \end {align*}

Solution by Maple

Time used: 0.017 (sec). Leaf size: 24

dsolve([diff(y(x),x)-y(x)*tan(x)=cos(x)-2*x*sin(x),y(1/6*Pi) = 0],y(x), singsol=all)
 

\[ y \relax (x ) = \frac {4 x \cos \left (2 x \right )-\pi +4 x}{8 \cos \relax (x )} \]

Solution by Mathematica

Time used: 0.082 (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*}