Internal problem ID [1995]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number: Problem 14.24 (b) .
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-y \tan \relax (x )-1=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {\pi }{4}\right ) = 3\right ] \end {align*}
✓ Solution by Maple
Time used: 0.02 (sec). Leaf size: 15
dsolve([diff(y(x),x)-y(x)*tan(x)=1,y(1/4*Pi) = 3],y(x), singsol=all)
\[ y \relax (x ) = \frac {\sin \relax (x )+\sqrt {2}}{\cos \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.051 (sec). Leaf size: 16
DSolve[{y'[x]-y[x]*Tan[x]==1,y[Pi/4]==3},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (\sin (x)+\sqrt {2}\right ) \sec (x) \\ \end{align*}