- #1
dooogle
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Homework Statement
dx/dt=x(1-2y) t(0)=0 x(t(0))=1
dy/dt=-y(1-2x), t(0)=0 y(t(0))=2
inerval of integration= [0,40]
Homework Equations
The Attempt at a Solution
i let x=p(t) so t=(p^-1)(x)
dy/dx=(∂y/∂(p^-1))∂(p^-1)/∂x
dy/dx=(-y(1-2x))/(x(1-2y))
since this equation is non homogeneous cannot make a substitution y=vx
the equation can be rearranged into the form
M(x,y)+N(x,y)dy/dx=0
where M(x,y)=y+2xy
and N(x,y)=x-2xy
but the equation is not exact as there is no function Ψ(x,y) such that
Ψx(x,y) =M(x,y) and Ψy(x,y)=N(x,y)
ive tried finding an integrating factor to make the equation exact using the formula
dμ/dx=μ((My-Nx)/N)
but My=1+2x
Nx=1-2y
((My-Nx)/N)=(1+2x-1-2y)/x-2xy
so
please could you tell me if i have made mistakes or point me in the direction i should be going
thank you for your time
dooogle