Internal problem ID [880]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 1, Introduction. Section 1.2 Page 14
Problem number: 5(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-\cos \relax (x )+y \tan \relax (x )=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {\pi }{4}\right ) = \frac {\sqrt {2}\, \pi }{8}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 8
dsolve([diff(y(x),x) = cos(x)-y(x)*tan(x),y(1/4*Pi) = 1/8*2^(1/2)*Pi],y(x), singsol=all)
\[ y \relax (x ) = x \cos \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.08 (sec). Leaf size: 9
DSolve[{y'[x] ==Cos[x]-y[x]*Tan[x],y[Pi/4]==Pi/(4*Sqrt[2])},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \cos (x) \\ \end{align*}