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 harley05 April 16th, 2015 03:17 AM

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

 topsquark April 16th, 2015 03:33 AM

Quote:
 Originally Posted by harley05 (Post 228821) 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

 harley05 April 16th, 2015 03:52 AM

thanks, yes it was a typo as you noticed. thanks again.

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