What is the solution for 3(sin(t)y^'+cos(t)y)=cos(t)sin^2(t) ?

The solution for 3(sin(t)y^'+cos(t)y)=cos(t)sin^2(t) is y=(sin^2(t))/9+(c_{1})/(sin(t))

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3(sin(t)y^'+cos(t)y)=cos(t)sin^2(t)

3 (sin (t) y^{^{'}} + cos (t) y) = cos (t) sin^{2} (t)

y = \frac{sin ^{2} ( t )}{9} + \frac{c _{1}}{sin ( t )}

Solution steps

3 (sin (t) y^{'} (t) + cos (t) y) = cos (t) sin^{2} (t)

Solve linear ODE:

y = \frac{sin ^{2} ( t )}{9} + \frac{c _{1}}{sin ( t )}

y = \frac{sin ^{2} ( t )}{9} + \frac{c _{1}}{sin ( t )}

\int arctan (9 x) d x

f (x) = \frac{1}{x} + \frac{1}{x ^{2}}

\frac{( 5 x ^{5} - 3 x ^{2} + 1 )}{x}

\int \frac{1}{12 ( x ^{2} + 1 )} d x

x \to 3 + lim (\frac{x}{x - 3})

What is the solution for 3(sin(t)y^'+cos(t)y)=cos(t)sin^2(t) ?
The solution for 3(sin(t)y^'+cos(t)y)=cos(t)sin^2(t) is y=(sin^2(t))/9+(c_{1})/(sin(t))