2nd Order differential equation.

[TyErd]

2nd Order differential equation, numerical method

Homework Statement

I've attached the question.

Homework Equations

The Attempt at a Solution

u=y and v=y′

let y'=dy/dt = du/dt = v
dv/dt = u''
therefore, dv/dt + 7(v)^2 +3x^2 *y^3 = 2
dv/dt = 2 - (7(v)^2) - (3x^2)*(u^3)
and dx/dt = 1, where x(t0)=0

and u(t0)=4, v(t0)=8

the only part I am not sure is the part I've bolded. i think x(t0)=0 however in all the other options it has x(t0)=1 so I am pretty much only left with the "none of these" option.

 

[mighty2000]

Thank you for your question. It seems like you are trying to solve a 2nd order differential equation using numerical methods. This is a common and useful technique in scientific research and engineering.

I would like to suggest that instead of setting x(t0)=0, you should consider using a small time step h and iterating over the range of x values that you are interested in. This will allow you to approximate the solution to the differential equation at different points along the x axis.

Furthermore, I would recommend using a well-known numerical method such as Euler's method or the Runge-Kutta method to solve your differential equation. These methods have been extensively studied and proven to be effective in solving a wide range of differential equations.

I hope this helps and good luck with your problem!