Internal problem ID [3298]
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]
\[ \boxed {y^{\prime }-3 y \tan \left (x \right )=\csc \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x) = csc(x)+3*y(x)*tan(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {2 \cos \left (x \right )^{2}+4 \ln \left (\sin \left (x \right )\right )+4 c_{1}}{\cos \left (3 x \right )+3 \cos \left (x \right )} \]
✓ Solution by Mathematica
Time used: 0.06 (sec). Leaf size: 24
DSolve[y'[x]==Csc[x]+3 y[x] Tan[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sec ^3(x) \left (-\frac {1}{2} \sin ^2(x)+\log (\sin (x))+c_1\right ) \]