Maple 9 Learning Guide - Maplesoft

3.6 Solving Differential Equations Using the dsolve Command • 71mean 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 6.2 Assumptions.3.6 Solving Differential Equations Using thedsolve CommandMaple can symbolically solve many ordinary differential equations (ODEs),including initial value and boundary value problems.Define an ODE. Note that the diff command and not the inert formDiff is used in this example.> 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 := {D(y)(0) = 1, y(0) = 0}Solve with dsolve by using the union operator to form the union ofthe two sets.> soln := dsolve(ode1 union ic, {y(t)});soln := y(t) = −e (−3 t) (−2 t)+ eTo evaluate the solution at points or plot it, first use the unapplycommand to define a proper Maple function. For more information, see3.1 The Maple solve Command.To extract a value from a solution set, use the eval command.