Section 5.3

# Section 5.3 - Differential Equations Texas A&M...

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Unformatted text preview: Differential Equations Texas A&M University Math 308, Spring 2008 c circlecopyrt F. Dos Reis Section 5.3 Definition: A system of m differentiable equations in m unknown functions x 1 ( t ) , · · · ,x m ( t ) is in the normal form if it is expressed as x ′ 1 ( t ) = f 1 ( t,x 1 , · · · ,x m ) x ′ 2 ( t ) = f 2 ( t,x 1 , · · · ,x m ) . . . x ′ m ( t ) = f m ( t,x 1 , · · · ,x m ) Exercise 1. Are those systems in the normal form? braceleftbigg x ′ ( t ) = y ′ ( t ) + 3 x ( t )- 5 y ( t ) y ′ ( t ) + x ′ ( t ) = 8 x ( t 0 + y ( t ) braceleftbigg x ′ = 11 x- 2 y y ′ = 5 x + 3 y Exercise 2. Given the initial value problem y ′′ + 3 y ′- 5 y = e − t y (0) = 1 ,y ′ (0) = 5 . Convert the initial value problem into a system of initial value problems in the normal form. Recall - Euler’s Method formulae for 1 differential equation: Given a differential equation y ′ = f ( x,y ), the initial condition y ( a ) = b and, the step size...
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Section 5.3 - Differential Equations Texas A&M...

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