Internal problem ID [2769]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 1
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-1+\cot \relax (x ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 15
dsolve(diff(y(x),x) = 1-y(x)*cot(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {-\cos \relax (x )+c_{1}}{\sin \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 15
DSolve[y'[x]==1-y[x]*Cot[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\cot (x)+c_1 \csc (x) \\ \end{align*}