Is it possible to obtain the expression on the right using only the laplace function of MATLAB to the expression on the left?

"L1 dI1/dt + M dI2/dt + 1/C1*int(I1 dτ) = E(t)" is the expression on the left while "1/ sqrt((r 2 − 1)^2 + 0.01)" is the expression on the right. There are no given values. Only the expressions are shown and by using the laplace function on the expression on the left, I should be able to obtain the expression on the right. Is it possible?

[Torsten]

"L1 dI1/dt + M dI2/dt + 1/C1*int(I1 dτ) = E(t)" is not an expression, but an equation.

You can't make an equation equal an expression.

So what do you mean exactly ?

[Harry Louise Plasabas]

Sorry, equation rather. I was tasked by my teacher to derive the expression on the right using the laplace function in MATLAB on the equation on the left. I was wondering, is it possible?

Answer 1

[Ishan]

To obtain the Laplace transformation on the left you would probably need to reduce your equation to be a function of t. However, judging by the equation, it seems to be that of an RLC circuit (not sure of constant M though). You can refer to the attached documentation to solve the differential equation though, provided there is a known relationship between I1 and I2(like using Kirchhoff’s law in case of an RLC circuit).

Solve Differential Equations Using Laplace Transform - MATLAB & Simulink - MathWorks India

To begin with, you can symbolically compute the Laplace transform of your given equation using this code snippet (it won’t give the expression on the right, but will serve as a starting point to solve the differential equation you might have) :-

syms L M C I1(t) I2(t) r
iI1 = int(I1,0,t); %integrate I1 w.r.t t
dI2 = diff(I2,t); %differentiate I2 w.r.t t
dI1 = diff(I1,t); %differentiate I1 w.r.t t
eqn1 = L*dI1 + M*dI2 + (1/C)*iI1; 
eqn1LT = laplace(eqn1,t,r)

eqn1LT =