cos(x)y^'+sin(x)y=2cos^3(x)sin(x)-1

解

cos (x) y^{^{'}} + sin (x) y = 2 cos^{3} (x) sin (x) - 1

y = - \frac{tan ( x )}{sec ( x )} - \frac{cos ( 2 x )}{2 sec ( x )} + \frac{c _{1}}{sec ( x )}

解答ステップ

cos (x) y^{'} (x) + sin (x) y = 2 cos^{3} (x) sin (x) - 1

線形 ODE を解く:

y = - \frac{tan ( x )}{sec ( x )} - \frac{cos ( 2 x )}{2 sec ( x )} + \frac{c _{1}}{sec ( x )}

y = - \frac{tan ( x )}{sec ( x )} - \frac{cos ( 2 x )}{2 sec ( x )} + \frac{c _{1}}{sec ( x )}