SecondOrder

# SecondOrder - Solving Second Order Differential Equations...

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Solving Second Order Differential Equations Math 308 This Maple session contains examples that show how to solve certain second order constant coefficient differential equations in Maple. Also, at the end, the "subs" command is introduced. First, we solve the homogeneous equation y'' + 2y' + 5y = 0. We'll call the equation "eq1": > eq1 := diff(y(t),t,t) + 2*diff(y(t),t) + 5*y(t) = 0; := eq1 = + + ± ² ² ³ ´ µ µ 2 t 2 ( ) y t 2 ± ² ² ³ ´ µ µ t ( ) y t 5 ( ) y t 0 We use the "dsolve" command to solve the differential equation. In its basic form, this command takes two arguments. The first is the differential equation, and the second is the function to be found. We'll use the "rhs" command to save the actual solution in the variable "sol1": > sol1 := rhs(dsolve(eq1,y(t))); := sol1 + _C1 e ( ) - t ( ) sin 2 t _C2 e ( ) - t ( ) cos 2 t The two expressions _C1 and _C2 are Maple's "arbitrary constants". That was easy enough. How do we specify initial conditions? Consider the initial value problem y'' + 2y' + 5y = 0, y(0)=3, y'(0)=-5. We use the "dsolve" command again, but we now make a list of the equation and the initial conditions. The first initial condition, y(0) =3, is written in Maple just as it is here. However, to enter the initial value of y', we can not simply write y'(0)=-5. The single quote ' has a special meaning in Maple, and it is not a derivative. Instead, we use the "D" operator. The operator "D" is another way to specify the derivative of a function. The derivative y'(t) can be expressed in Maple as D(y)(t).

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## This note was uploaded on 02/11/2012 for the course MTH 141, 142, taught by Professor Mcallister during the Spring '08 term at SUNY Empire State.

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SecondOrder - Solving Second Order Differential Equations...

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