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## Homework Statement

https://webwork.utpa.edu/webwork2_files/tmp/equations/2d/02a7e6a06f5b2424758fa01cc965f71.png [Broken]

**with**https://webwork.utpa.edu/webwork2_files/tmp/equations/80/81c176aa8964438a63eb096513245f1.png [Broken]

## Homework Equations

[/B]

Standard form: y' + p(x)y = f(x)

Integrating factor: r(x)= e

^{∫p(x)dx}

Solution: y(x) = e

^{-∫p(x)dx}(∫e

^{∫p(x)dx}⋅ f(x) dx + C)

## The Attempt at a Solution

From, y' - y = 7e

^{t}+ 56e

^{8t}

I got, p(x) = -1 and f(x) = 7e

^{t}+ 56e

^{8t}

So the integrating factor is r(t)= e

^{∫-1 dt}= e

^{-t}

Plug it into the solution formula,

y(t)= e

^{t}

**[**∫e

^{-t}(7e

^{t}+ 56e

^{8t}) dt + C

**]**

= e

^{t}(7t + 8e

^{7t}+ C)

= 7te

^{t}+ 8e

^{8t}+ Ce

^{t}

Using the initial condition y(0)= 2

= 8 + C = 2

C = -6

My final solution,

y(t) = 7te

^{t}+ 8e

^{8t}- 6e

^{t}

check: y(0) = 7(0)e

^{(0)}+ 8e

^{8(0)}- 6e

^{(0)}= 2

But when I type it into WeBWork, it says my answer is incorrect. I don't think its a syntax problem because it has a preview button that allows you to see your actual problem.

Could it be that, y' - y = 7e

^{t}+ 56e

^{8t}is not in standard form?

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