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## Homework Statement

Solve each of these differential equations by two different methods.

[tex] \frac{dy}{dx} = 4(y+1)x^3[/tex]

## Homework Equations

Integrating factor

[tex] \rho = \exp (\int(p(x) dx)[/tex]

Linear Equation

[tex] \frac{dy}{dx} + p(x) y(x) = Q(x) [/tex]

## The Attempt at a Solution

So I first solved it using separation. I get [tex] y=A \exp(x^4) -1 [/tex]

I then try to solve it using Integrating factors.

[tex] \frac{dy}{dx} + - 4x^3 y=4x^3 [/tex]

[tex] \rho = \exp (\int -4x^3 dx) = exp(-x^4) [/tex]

Multiplying through by the integrating factor I get.

[tex] \exp(-x^4) y= \int 4x^3 exp(-x^4) dx [/tex]

but when I solve it, I get

[tex] y = -1 [/tex]

What can I be doing wrong? I checked my steps multiple times.