Differential Equation: dy/dx=-2x/y . Let y=f(x) be the particular solution to the differential equation with the initial condition f(1)=-1. Write an equation for the line tangent to the graph of f at (1,-1) and use it to approximate f(1.1).
Find the particular solution y=f(x) to the differential equation with the initial condition f(1)=-1.

Question

Differential Equation: dy/dx=-2x/y . Let y=f(x) be the particular solution to the differential equation with the initial condition f(1)=-1. Write an equation for the line tangent to the graph of f at (1,-1) and use it to approximate f(1.1). 
Find the particular solution y=f(x) to the differential equation with the initial condition f(1)=-1.

darkigloo · Answer

I don't know how to start this problem.

anonymous · Answer

hint: separable differential equations

darkigloo · Answer

int (ydy)= int (-2xdx) ?

anonymous · Answer

yes, integrate both sides. DOn't forget the constant

darkigloo · Answer

But is that for the second part of the question, to find the solution y=f(x) with initial condition f(1)=-1?

anonymous · Answer

(y - yi) = m (x - xo) 
you're given a point. So now you just need to know slop. 
m = dy/dx = -2x/y. Plugs in the given point.

darkigloo · Answer

would that be y+1=2(x-1) ?

anonymous · Answer

yes

darkigloo · Answer

so how do I use that to approximate f(1.1)?

anonymous · Answer

plug 1.1 in for x

darkigloo · Answer

so the approximation of f(1.1) is -0.8?

anonymous · Answer

if you did the math right

darkigloo · Answer

ok thanks.