ODE
\[ y'(x)=3 y(x) \tan (x)+\csc (x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.173654 (sec), leaf count = 24
\[\left \{\left \{y(x)\to \sec ^3(x) \left (-\frac {1}{2} \sin ^2(x)+\log (\sin (x))+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.082 (sec), leaf count = 39
\[\left [y \left (x \right ) = \frac {\cos \left (2 x \right )+1+2 \ln \left (\cos \left (x \right )-1\right )+2 \ln \left (1+\cos \left (x \right )\right )+4 \textit {\_C1}}{\cos \left (3 x \right )+3 \cos \left (x \right )}\right ]\] Mathematica raw input
DSolve[y'[x] == Csc[x] + 3*Tan[x]*y[x],y[x],x]
Mathematica raw output
{{y[x] -> Sec[x]^3*(C[1] + Log[Sin[x]] - Sin[x]^2/2)}}
Maple raw input
dsolve(diff(y(x),x) = csc(x)+3*y(x)*tan(x), y(x))
Maple raw output
[y(x) = (cos(2*x)+1+2*ln(cos(x)-1)+2*ln(1+cos(x))+4*_C1)/(cos(3*x)+3*cos(x))]