Internal problem ID [5134]
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]
\[ \boxed {y^{\prime }+y \cot \left (x \right )=\cos \left (x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 8
dsolve([diff(y(x),x)+y(x)*cot(x)=cos(x),y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\sin \left (x \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.103 (sec). Leaf size: 11
DSolve[{y'[x]+y[x]*Cot[x]==Cos[x],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\sin (x)}{2} \]