Internal problem ID [15139]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 12. Miscellaneous problems. Exercises page 93
Problem number: 277.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {y^{\prime }+\cos \left (x \right ) y-y^{n} \sin \left (2 x \right )=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 49
dsolve(diff(y(x),x)+y(x)*cos(x)=y(x)^n*sin(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \left (\frac {{\mathrm e}^{\sin \left (x \right ) \left (n -1\right )} c_{1} n -{\mathrm e}^{\sin \left (x \right ) \left (n -1\right )} c_{1} +2 \sin \left (x \right ) n -2 \sin \left (x \right )+2}{n -1}\right )^{-\frac {1}{n -1}} \]
✓ Solution by Mathematica
Time used: 6.877 (sec). Leaf size: 36
DSolve[y'[x]+y[x]*Cos[x]==y[x]^n*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \left (c_1 e^{(n-1) \sin (x)}+\frac {2}{n-1}+2 \sin (x)\right ){}^{\frac {1}{1-n}} \]