PhysicsCat
New member
- Joined
- May 1, 2023
- Messages
- 5
Hello!
I have the following task:
" Solve the initial value problem
[math]x^{\prime \prime} - 2x^{\prime} +2x = e^{2t} \sin(t)[/math] with [math]x(0) = \frac{3}{5}[/math] and [math]x^{\prime}(0) = 1[/math]"
I solved the homogenous problem and got to the solution [imath]x_h(t) = e^t \cos(t) (c_1 + c_2)[/imath], where [imath]c_1[/imath] and [imath]c_2[/imath] are constants.
This solution does solve the homogenous problem, but now Im stuck with the inhomogeneous problem. I had the idea of using the variation of constants, but considering I have two different constants, that scared me a bit. Is there a better way to solve the inhomogeneous problem in this case?
Thank you very much and have a nice day!
I have the following task:
" Solve the initial value problem
[math]x^{\prime \prime} - 2x^{\prime} +2x = e^{2t} \sin(t)[/math] with [math]x(0) = \frac{3}{5}[/math] and [math]x^{\prime}(0) = 1[/math]"
I solved the homogenous problem and got to the solution [imath]x_h(t) = e^t \cos(t) (c_1 + c_2)[/imath], where [imath]c_1[/imath] and [imath]c_2[/imath] are constants.
This solution does solve the homogenous problem, but now Im stuck with the inhomogeneous problem. I had the idea of using the variation of constants, but considering I have two different constants, that scared me a bit. Is there a better way to solve the inhomogeneous problem in this case?
Thank you very much and have a nice day!