Suppose you want to find an equation for a curve that passes through the point(1, 2) and whose slope at any point (x, y) is 2x^3/y .

You d solve the differential equation dy/dx = 2x^3/y with initial condition y(1) = 2.
Solving this differential equation with initial condition, you get: (see attachment)

Question

Suppose you want to find an equation for a curve that passes through the point(1, 2) and whose slope at any point (x, y) is 2x^3/y .

You d solve the differential equation dy/dx = 2x^3/y with initial condition y(1) = 2. 
Solving this differential equation with initial condition, you get: (see attachment)

anonymous · Answer

attachment

myininaya · Answer

So this can be solved by separation of variables
We want to write g(y) dy=f(x) dx
And then we can integrate both sides

myininaya · Answer

$$\frac{dy}{dx}=\frac{2x^3}{y}$$

Multiply y on both sides
Multiply dx on both sides
What is the resulting equation once that has been done?

anonymous · Answer

B?

myininaya · Answer

$$y dy=2x^3 dx$$
See how I multiplied y and dx on both sides
now I integrate both sides
given me
$$\frac{y^2}{2}=\frac{2x^4}{4}+C$$
$$y^2=2(\frac{2x^4}{4})+C$$
Then use y(1)=2 to find C
So plug 1 in for x and 2 in for y
and solve for C