Internal problem ID [2789]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 2
Problem number: 34.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-\csc \relax (x )-3 y \tan \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(diff(y(x),x) = csc(x)+3*y(x)*tan(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {2 \ln \left (\cos \relax (x )-1\right )+2 \ln \left (1+\cos \relax (x )\right )+\cos \left (2 x \right )+1+4 c_{1}}{\cos \left (3 x \right )+3 \cos \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.068 (sec). Leaf size: 24
DSolve[y'[x]==Csc[x]+3 y[x] Tan[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sec ^3(x) \left (-\frac {1}{2} \sin ^2(x)+\log (\sin (x))+c_1\right ) \\ \end{align*}