Learning Guide Learning Guide

70 • Chapter 3: Finding Solutionsmean a~. In Maple, single quotes delay evaluation. In this case, theyensure that Maple interprets the second a as a and not as a~.Now that you have removed the assumption on a inside ans, you canremove the assumption on a itself by assigning it to its own name.> a := ’a’:Use single quotes here to remove the assumption on a. For more informationon assumptions, see section 5.2.3.6 Differential Equations: dsolveMaple can symbolically solve many ordinary differential equations (ODEs),including initial value and boundary value problems.Define an ODE.> ode1 := {diff(y(t),t,t) + 5*diff(y(t),t) + 6*y(t) = 0};ode1 := {( d2dt 2 y(t)) + 5 ( d y(t)) + 6 y(t) = 0}dtDefine initial conditions.> ic := {y(0)=0, D(y)(0)=1};ic := {y(0) = 0, D(y)(0) = 1}Solve with dsolve, using the union operator to form the union of thetwo sets.> soln := dsolve(ode1 union ic, {y(t)});soln := y(t) = −e (−3 t) (−2 t)+ eIf you want to evaluate the solution at points or plot it, remember touse the unapply command to define a proper Maple function. For moreinformation, see section 3.1.You can conveniently extract a value from a solution set with the aidof eval.> eval( y(t), soln );