Internal problem ID [4593]
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: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }+y \cot \relax (x )-5 \,{\mathrm e}^{\cos \relax (x )}=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {\pi }{2}\right ) = -4\right ] \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 16
dsolve([diff(y(x),x)+y(x)*cot(x)=5*exp(cos(x)),y(1/2*Pi) = -4],y(x), singsol=all)
\[ y \relax (x ) = \frac {-5 \,{\mathrm e}^{\cos \relax (x )}+1}{\sin \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.199 (sec). Leaf size: 16
DSolve[{y'[x]+y[x]*Cot[x]==5*Exp[Cos[x]],{y[Pi/2]==-4}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (1-5 e^{\cos (x)}\right ) \csc (x) \\ \end{align*}