What is the solution for y=x^3*e^{-2x}cos(3x)(dy)/(dx) ?

The solution for y=x^3*e^{-2x}cos(3x)(dy)/(dx) is y=e^{integral of 1/(e^{-2x)x^3cos(3x)}}

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y=x^3*e^{-2x}cos(3x)(dy)/(dx)

y = x^{3} \cdot e^{- 2 x} cos (3 x) \frac{d y}{d x}

y = e^{\int \frac{1}{e ^{- 2 x} x ^{3} c o s ( 3 x )} d x}

Solution steps

y = x^{3} \cdot e^{- 2 x} cos (3 x) \frac{d y}{d x}

Solve separable ODE:

y = e^{\int \frac{1}{e ^{- 2 x} x ^{3} c o s ( 3 x )} d x}

y = e^{\int \frac{1}{e ^{- 2 x} x ^{3} c o s ( 3 x )} d x}

(3 y) d x + (2 x) d y = 0

t^{- 1} \frac{d y}{d t} = 8 cos^{2} (y), y (2) = \frac{3 π}{4}

y^{^{'}} + sin (y) = 0

\frac{d x}{d t} = - 9000 + \frac{7.5}{100} x

2 y y^{^{'}} = 9 t^{2}, y (0) = 2

What is the solution for y=x^3*e^{-2x}cos(3x)(dy)/(dx) ?
The solution for y=x^3*e^{-2x}cos(3x)(dy)/(dx) is y=e^{integral of 1/(e^{-2x)x^3cos(3x)}}