`dy/dx = 5 - 8x` Solve the differential equation

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`(dy)/dx=5-8x`

This differential equation is separable since it has a form

  • `N(y) (dy)/dx=M(x)`

And, it can be re-written as

  • `N(y) dy = M(x) dx`

So separating the variables, the equation becomes

`dy=(5-8x)dx`

Integrating both sides, it result to

`int dy = int (5-8x)dx`

`y + C_1 = 5x - (8x^2)/2...

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`(dy)/dx=5-8x`

This differential equation is separable since it has a form

  • `N(y) (dy)/dx=M(x)`

And, it can be re-written as

  • `N(y) dy = M(x) dx`

So separating the variables, the equation becomes

`dy=(5-8x)dx`

Integrating both sides, it result to

`int dy = int (5-8x)dx`

`y + C_1 = 5x - (8x^2)/2 + C_2`

`y+ C_1 = 5x - 4x^2 + C_2`

Isolating the y, it becomes

`y = 5x - 4x^2 + C_2 -C_1`

Since C2 and C1 are constants, it can be expressed as a single constant C.

`y=5x-4x^2+C`

`y=-4x^2 + 5x + C`

Therefore, the general solution of the given differential equation is `y=-4x^2 + 5x + C` .

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