What is the solution for (dy)/(dx)+7x^6y=x^6 ?

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

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(dy)/(dx)+7x^6y=x^6

\frac{d y}{d x} + 7 x^{6} y = x^{6}

y = \frac{e ^{- x^{7} + c_{1}}}{7} + \frac{1}{7}

Solution steps

\frac{d y}{d x} + 7 x^{6} y = x^{6}

Solve separable ODE:

y = \frac{e ^{- x^{7} + c_{1}}}{7} + \frac{1}{7}

y = \frac{e ^{- x^{7} + c_{1}}}{7} + \frac{1}{7}

\frac{2 x + 4 x ^{2}}{( 1 + 4 x ) ^{2}}

\frac{d}{d x} (e^{k^{2} x})

\frac{d}{d x} (\frac{( x + 4 ) ^{2}}{x + 3})

(x^{2} + 1) y^{^{''}} + 2 x y^{^{'}} = 0

y d x - (y - x) d y = 0

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