What is the solution for ((dy))/((dx)-3y)=x^{(6)} ?

The solution for ((dy))/((dx)-3y)=x^{(6)} is y=-(e^{(-3x^7-c_{1})/7})/(3)+1/3

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((dy))/((dx)-3y)=x^{(6)}

\frac{( d y )}{( d x ) - 3 y} = x^{(6)}

y = - \frac{e ^{\frac{- 3 x ^{7} - c _{1}}{7}}}{3} + \frac{1}{3}

Solution steps

\frac{( d y )}{( d x ) - 3 y} = x^{(6)}

Solve separable ODE:

y = - \frac{e ^{\frac{- 3 x ^{7} - c _{1}}{7}}}{3} + \frac{1}{3}

y = - \frac{e ^{\frac{- 3 x ^{7} - c _{1}}{7}}}{3} + \frac{1}{3}

\frac{d x}{sin ( y )} + \frac{d y}{cos ( x )} = 0

x^{6} y^{^{'}} + 13 x^{5} y = 0

y^{^{'}} x = (1 - y^{2})^{\frac{1}{2}}

y^{^{'}} - x^{5} y^{4} = 0, y (0) = 2, y (2) = a

2 y^{^{'}} - y y^{^{'}} = x^{2} + 1

What is the solution for ((dy))/((dx)-3y)=x^{(6)} ?
The solution for ((dy))/((dx)-3y)=x^{(6)} is y=-(e^{(-3x^7-c_{1})/7})/(3)+1/3