Satisfy the Differential Equation - Linear Equation

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SUMMARY

The differential equation dy/dx - 3y = 6e^(5x) is solved using the integrating factor method, where P(x) = -3 and the integrating factor is e^(-3x). The solution derived is y = e^(3x)(3e^(2x) - 9) after integrating both sides and determining the constant C = -9. The issue encountered with Webwork arises from the requirement for the variable 't' instead of 'x' for input, despite the solution being mathematically correct.

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Homework Statement



Find the function satisfying the differential equation:

dy/dx - 3y = 6e^(5x)

with y(0) = -6

Homework Equations



I believe this is Linear, so it is dy/dx + P(x)y = f(x)

The Attempt at a Solution



I chose -3y to be P and used it to obtain integrating factor e^(-3x). I multiplied it though and ended up with d/dx(e^(-3x)y) = 6e^(2x)

I integrated both sides and got e^(-3x)y = 3e^2x + C

Solving for C gets me -9 so the satisfying function is y=e^(3x)(3e^(2x)-9)

When I try to input this function into Webwork (online homework), it tells me it is incorrect and that the variable 'x' is not defined in this context.

I wanted to make sure I am correct or if somehow, x comes out of this equation.
 
Last edited:
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I've confirmed that this is correct. The online program wanted a t variable, not x.
 

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