What is the solution for dy=(4x-6)dx ?

The solution for dy=(4x-6)dx is y=2x^2-6x+c_{1}

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dy=(4x-6)dx

d y = (4 x - 6) d x

y = 2 x^{2} - 6 x + c_{1}

Solution steps

d y = (4 x - 6) d x

Let

y

be the dependent variable. Divide by

d x

\frac{d y}{d x} = 4 x - 6

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = 4 x - 6

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int 4 x - 6 d x

\int 4 x - 6 d x = 2 x^{2} - 6 x + c_{1}

y = 2 x^{2} - 6 x + c_{1}

\frac{d y}{d x} + \frac{1}{3} y = \frac{1}{3} (1 - 2 x) y^{4}

x^{4} \frac{d y}{d x} - 2 x^{3} y = 4 x^{6} - 3 x^{2}

\int \frac{x ^{2} - 196}{x} d x

\int \frac{1}{x ^{2} - a ^{2}} d x

x \to 0 + lim (arctan (x))

What is the solution for dy=(4x-6)dx ?
The solution for dy=(4x-6)dx is y=2x^2-6x+c_{1}