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*}