hello
I am trying to solve this 2nd order linear inhomogeneous ordinary differential equation
[math]\frac{40}{17}x''-\frac{1}{17}x'+0.4x=6-\frac{123}{25}e^{-0.18t}[/math]
In order to solve this I need a particular integral for f(t) right( which is the rhs)
I know how to write the particular integral for the exponential and constant terms individually. But I don't know how I should do it when they're together like this.
So far I attempted to write the particular integral as:
[math]\lambda_{1}+\lambda_{2}e^{kx}[/math]assuming I just need to sum the individual particular integrals for the constant and exponential terms just as they are summed in the ode.
is this the correct choice?
I am trying to solve this 2nd order linear inhomogeneous ordinary differential equation
[math]\frac{40}{17}x''-\frac{1}{17}x'+0.4x=6-\frac{123}{25}e^{-0.18t}[/math]
In order to solve this I need a particular integral for f(t) right( which is the rhs)
I know how to write the particular integral for the exponential and constant terms individually. But I don't know how I should do it when they're together like this.
So far I attempted to write the particular integral as:
[math]\lambda_{1}+\lambda_{2}e^{kx}[/math]assuming I just need to sum the individual particular integrals for the constant and exponential terms just as they are summed in the ode.
is this the correct choice?