Satisfy the Differential Equation - Linear Equation

TrueStar
Messages
94
Reaction score
0

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:
Physics news on Phys.org
I've confirmed that this is correct. The online program wanted a t variable, not x.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top