I need to find out how to find the time function of $OUT1$ and $OUT2$ in my circuit
The LTSpice software shows no problem at all when solving this,
but unfortunately, it only shows the graphs, not the functions
I want to solve this using nodal analysis
I have tried using Microsoft Mathematics, Symbolab, and any other online differential equation solver, but it cannot solve it.
Is there any way how to calculate the function?
There are three conditions:
- before the switch is closed
- while the switch is closed
- after the switch is closed
I think, i need to solve it sequentially, because the system has a memory
Here are the system equations (before the switch is closed):
$\Large\frac{9+9}{R_6+R_9}+\frac{9-V_d}{R_4}+\frac{9-V_c}{R_1}=0$
$\Large\frac{V_d-9}{R_4}+\frac{V_d-V_c}{R_8}+\frac{V_d}{R_5}+\frac{V_d-V_d⋅{(1-e^{-\frac t{R_7⋅C_2}})}}{R_7}=0$
$\Large\frac{V_c-9}{R_1}+\frac{V_c-V_d}{R_8}+\frac{V_c}{R_2}+\frac{V_c-V_c⋅{(1-e^{-\frac t{R_3⋅C_1}})}}{R_3}=0$
Based on your comments, it appears that the answer is “this is not a differential equation.” A differential equation is one that contains an expression for a function involving (amongst other things) its derivatives, such as $y’=y+x$. This is a differential equation because $\frac{d}{dx}y=y’$. Your equation didn’t seem to involve any derivatives, and so is not a differential equation.
It also seems like the system of equations you’ve described is severely underdetermined. Are there more equations you left out of your post? A system of equations with 10 unknowns needs to have 10 equations to have a unique solution.