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April 16th, 2015, 03:17 AM   #1
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Ode

Hi, just want to check if i have obtained the correct answer for the question below:
dy/dt = 4y (x^3 - 1/2);
a) Find ODE solution subject to initial conditions y(1) = 3/e.
b) Find y(-1)

Ans (a)
For the general solution i get, y = Ce^(x^4 - 2x)
At initial condition y(1) = 3/e
y =3e^(x^4 - 2x)

Ans (b)
3e

thanks in advance
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April 16th, 2015, 03:33 AM   #2
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Quote:
Originally Posted by harley05 View Post
Hi, just want to check if i have obtained the correct answer for the question below:
dy/dt = 4y (x^3 - 1/2);
a) Find ODE solution subject to initial conditions y(1) = 3/e.
b) Find y(-1)

Ans (a)
For the general solution i get, y = Ce^(x^4 - 2x)
At initial condition y(1) = 3/e
y =3e^(x^4 - 2x)

Ans (b)
3e

thanks in advance
A question about your ODE: Is this supposed to be dy/dx = ... or is x a function of t as well?

-Dan

Edit: Yup. It's a typo. You have the correct solution, but look at y(-1) again. $\displaystyle y(-1) = 3 \cdot exp((-1)^4 - 2(-1)) = 3 \cdot exp(1 + 2) = 3e^3$.

-Dan
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Last edited by topsquark; April 16th, 2015 at 03:38 AM.
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April 16th, 2015, 03:52 AM   #3
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thanks, yes it was a typo as you noticed. thanks again.
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