What is the solution for 7(sin(t)y^'+cos(t)y)=cos(t)sin^3(t) ?

The solution for 7(sin(t)y^'+cos(t)y)=cos(t)sin^3(t) is y=(sin^3(t))/(28)+(c_{1})/(sin(t))

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

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

y = \frac{sin ^{3} ( t )}{28} + \frac{c _{1}}{sin ( t )}

Solution steps

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

Solve linear ODE:

y = \frac{sin ^{3} ( t )}{28} + \frac{c _{1}}{sin ( t )}

y = \frac{sin ^{3} ( t )}{28} + \frac{c _{1}}{sin ( t )}

\frac{d y}{d x} = \frac{- 2 x}{y}, y (0) = 1

\frac{d}{d x} (6 x + e^{- x})

(x^{2} y - x) d y + y d x = 0

\frac{d}{d x} (\frac{10}{x ^{7}})

y = 9 x, y = \frac{1}{3} x, y = 10 - x^{2}

What is the solution for 7(sin(t)y^'+cos(t)y)=cos(t)sin^3(t) ?
The solution for 7(sin(t)y^'+cos(t)y)=cos(t)sin^3(t) is y=(sin^3(t))/(28)+(c_{1})/(sin(t))