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

The solution for (dy)/(dx)=-2/(x^3)+2e^{2x-2} is y= 1/(x^2)+e^{2x-2}+c_{1}

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(dy)/(dx)=-2/(x^3)+2e^{2x-2}

\frac{d y}{d x} = - \frac{2}{x ^{3}} + 2 e^{2 x - 2}

y = \frac{1}{x ^{2}} + e^{2 x - 2} + c_{1}

Solution steps

\frac{d y}{d x} = - \frac{2}{x ^{3}} + 2 e^{2 x - 2}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = - \frac{2}{x ^{3}} + 2 e^{2 x - 2}

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

then

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

y = \int - \frac{2}{x ^{3}} + 2 e^{2 x - 2} d x

\int - \frac{2}{x ^{3}} + 2 e^{2 x - 2} d x = \frac{1}{x ^{2}} + e^{2 x - 2} + c_{1}

y = \frac{1}{x ^{2}} + e^{2 x - 2} + c_{1}

f (x) = 2 x^{2} + 5 x^{2} - 2, at x = 2

y = x^{2} + 6

\int_{- 1}^{1} x^{3} - x d x

\int \frac{sin ^{2} ( x )}{4} d x

\int_{0}^{\infty} sin^{2} (x) d x

What is the solution for (dy)/(dx)=-2/(x^3)+2e^{2x-2} ?
The solution for (dy)/(dx)=-2/(x^3)+2e^{2x-2} is y= 1/(x^2)+e^{2x-2}+c_{1}