Math Help - first order autonomous eq

1. first order autonomous eq

Hello
I have a question so if someone can help me:

Solve the autonmous problem
dx/dt= y,
dy/dt= 4x
by viewing y as a function of x with dy/dx=4x/y
inital conditions:
x(0) = 1, y(0) = 10

Jewons

2. Originally Posted by jewons
Hello
I have a question so if someone can help me:

Solve the autonmous problem
dx/dt= y,
dy/dt= 4x
by viewing y as a function of x with dy/dx=4x/y
inital conditions:
x(0) = 1, y(0) = 10

Jewons
Well, dy/dx= 4x/y is separable, isn't it? Integrate both sides of ydy= 4xdx and then use the fact that y= 10 when x= 0 to determine the constant of integration.

3. hello

I have tried to do that and I have some algebraic problem then
What I get when integrate bothe parts is y^2/2=4x^2/2 +c
or y^2=4x2+c but I do not know how to proceed than?