Learning Guide Learning Guide

72 • Chapter 3: Finding SolutionsIf you want to change the differential equation, or the definition ofy(t), then you can remove the definition with the following command.> y := ’y’;y := yMaple also understands special functions, such as the Dirac delta orimpulse function, used in physics.> ode2 := 10^6*diff(y(x),x,x,x,x) = Dirac(x-2) -> Dirac(x-4);ode2 := 1000000 ( d4y(x)) = Dirac(x − 2) − Dirac(x − 4)dx4 Specify boundary conditions> bc := {y(0)=0, D(D(y))(0)=0, y(5)=0};bc := {y(0) = 0, y(5) = 0, (D (2) )(y)(0) = 0}and an initial value.> iv := {D(D(y))(5)=0};iv := {(D (2) )(y)(5) = 0}> soln := dsolve({ode2} union bc union iv, {y(x)});1soln := y(x) = Heaviside(x − 2) x360000001−750000 Heaviside(x − 2) + 1Heaviside(x − 2) x5000001− Heaviside(x − 2) x210000001−6000000 Heaviside(x − 4) x3 + 1 Heaviside(x − 4)937501−125000 Heaviside(x − 4) x + 1Heaviside(x − 4) x2500000−115000000 x3 +11250000 x