2.48 problem 48

Internal problem ID [4626]

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: 48.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {y^{\prime }+y \cot \relax (x )-\cos \relax (x )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}

Solution by Maple

Time used: 0.187 (sec). Leaf size: 8

dsolve([diff(y(x),x)+y(x)*cot(x)=cos(x),y(0) = 0],y(x), singsol=all)
 

\[ y \relax (x ) = \frac {\sin \relax (x )}{2} \]

Solution by Mathematica

Time used: 0.161 (sec). Leaf size: 11

DSolve[{y'[x]+y[x]*Cot[x]==Cos[x],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {\sin (x)}{2} \\ \end{align*}