Solving differential equations with step functions

Solving differential equations with step functions

Lessons

We can use Laplace Transforms to solve second order differential equations with step functions

The following formulas may be needed:

LL{yy''} = s2s^{2}LL{yy} - s yy(0) - yy'(0)

LL{yy'} = s LL{yy} - yy(0)

LL{uc(t)u_{c}(t)f(tc)f(t - c)} = esce^{-sc}LL{f(t)f(t)}

  • 1.
    Solving Differential Equations with Step Functions Using the Laplace Transform

    Solve the following differential equation:

    3y2y+2y=22u2(t)3y'' - 2y' + 2y = 2 - 2u_{2}(t)

    Using initial conditions yy(0) = 3, yy'(0) = 2