# Differential equation

Find the particular solution of the following differential equation:

12(d^2y/dt^2)-3y=0

given that when t=0, y=3 and dy/dt=0.5

and could you explain the reasons for choosing y=e^(rt).

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Find the particular solution of the following differential equation

12(d2y/dt2) - 3y=0

given that when t=0, y=3 and dy/dt=0.5

Choosing y = ert simply by ...

#### Solution Summary

This solution provides an example of finding a particular solution for a differential equation.

Solving Difference Equation and Differential Equation

1. Complex Exponentials: Simply the following expression and give your answer both in polar and rectangular form.

o c=3ejπ/4+4e−jπ/2

2. Difference Equations: Solve the following difference equation using recursion by hand (for n=0 to n=4)

o y[n] + 0.5y[n-1] = 2x[n-1]; x[n] = δ[n], y[-1] = 0

3. Differential Equations: Solve the following problem for y(t).

o dy/dt + 2y(t) = 2x(t); x(t) = u(t), y(0) = −1