- #1

- 5

- 0

y'' + 4y = x , 0<=x<π

y'' + 4y = πe^-x , π<=x

Initial Conditions:

y(0)=0 y'(0)=1

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- Thread starter Loadme
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- #1

- 5

- 0

y'' + 4y = x , 0<=x<π

y'' + 4y = πe^-x , π<=x

Initial Conditions:

y(0)=0 y'(0)=1

- #2

Integral

Staff Emeritus

Science Advisor

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Sorry we do not do that here.

Start by applying Laplace tranforms to each of the equations.

Start by applying Laplace tranforms to each of the equations.

- #3

- 275

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and you will know what to do :)

also your ODE can be written using the step (Heaviside) function:

y'' + 4y = x + H[x-π](πe^(-x) - x)

H[x-π] = 0 at x<π; H[x-π] = 1 at x>=π;

Good Luck.

- #4

HallsofIvy

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Homework Helper

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No "full answer" but:

y'' + 4y = x , 0<=x<π

y'' + 4y = πe^-x , π<=x

Initial Conditions:

y(0)=0 y'(0)=1

1) Solve y"+ 4y= x, 0<= x< [itex]\pi[/itex]

with initial conditions y(0)= 0, y'(0)= 1.

Evaluate the function, [itex]y_1(x)[/itex], satifying those conditions and its derivative at [itex]x= \pi[/itex] and solve

2) [itex]y''[/itex][itex]+ 4y= [/itex][itex]\pi e^{-x}[/itex]

with initial conditions [itex]y(\pi)= y_1(\pi)[/itex], [itex]y'(\pi)= y_1'(\pi)[/itex].

- #5

- 5

- 0

How I would do it(and correct me where I am wrong)

y'' + 4y = x[u(x-0)-u(x-π)] + πe^(-x)*u(x-π)

How do you apply the Heavyside? Can you explain me your technique?

- #6

- 30

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You need to transform the equation. What have you got so far?

- #7

HallsofIvy

Science Advisor

Homework Helper

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