1.9 problem 9

Internal problem ID [1878]

Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 5, page 21
Problem number: 9.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_separable]

Solve \begin {gather*} \boxed {y^{\prime } \tan \relax (x )-y-1=0} \end {gather*}

Solution by Maple

Time used: 0.014 (sec). Leaf size: 10

dsolve(diff(y(x),x)*tan(x)-y(x)=1,y(x), singsol=all)
 

\[ y \relax (x ) = c_{1} \sin \relax (x )-1 \]

Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 17

DSolve[y'[x]*Tan[x]-y[x]==1,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -1+c_1 \sin (x) \\ y(x)\to -1 \\ \end{align*}