Question

Using the Laplace transform to solve the following system of ODEs x'+2x-y' = 0 x'+x+y = t² x(0) = y(0) = 0 Hint: r(s)/s³(s²+2s+0) = A/s+B/s²+C/s³+Ds+E/s²+2s+2

Answer 1

Mathematics problem involving solving a system of ODEs using Laplace transforms with an emphasis on partial fraction decomposition in the s-domain.

Step-by-step explanation:

The subject of the question is the application of Laplace transforms to solve a system of ordinary differential equations (ODEs). To solve these types of problems in Mathematics, we need to follow several steps. One approach is to begin by performing the Laplace transform on both sides of each equation and then using initial conditions to solve for unknowns in the s-domain. After that, partial fraction decomposition can be applied to break down complex fractions, which allows us to find the inverse Laplace transform and thus, the solution of the ODE in the time domain. This specific question implies the use of partial fraction decomposition in the s-domain, which involves finding constants that satisfy the given equation.