Internal problem ID [2503]
Book: Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section: Exercises, page 14
Problem number: 2(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-y \tan \relax (x )-x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve([diff(y(x),x)-y(x)*tan(x)=x,y(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {\cos \relax (x )+\sin \relax (x ) x -1}{\cos \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 15
DSolve[{y'[x]-y[x]*Tan[x]==x,y[0]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \tan (x)-\sec (x)+1 \\ \end{align*}