- #1
keith river
- 15
- 0
dy/dx = x/y
Solve the equation (get general form of y) for the given condition y=1 and x=2
I've tried finding the complementary function, dy/dx = 0.
So I assume y = C (a constant)
Now I'm trying the find the particular Integral.
dy/dx = x/y
rearrange for LHS containing only y and RHS containing only x
dy y = dx x
I integrate I get (y^2) / 2 = (x^2)/2 + D(constant due to integration)
y^2 = 2(x^2)/2 + 2D
y^2 = (x^2) + E (2D= E)
y = Sqrt (x^2) + Sqrt (E)
y = x + F
General function
y = C + x + F
y = G + x
The answer (given onnsheet) is y = Sqrt ((x^2) - 4)
Solve the equation (get general form of y) for the given condition y=1 and x=2
I've tried finding the complementary function, dy/dx = 0.
So I assume y = C (a constant)
Now I'm trying the find the particular Integral.
dy/dx = x/y
rearrange for LHS containing only y and RHS containing only x
dy y = dx x
I integrate I get (y^2) / 2 = (x^2)/2 + D(constant due to integration)
y^2 = 2(x^2)/2 + 2D
y^2 = (x^2) + E (2D= E)
y = Sqrt (x^2) + Sqrt (E)
y = x + F
General function
y = C + x + F
y = G + x
The answer (given onnsheet) is y = Sqrt ((x^2) - 4)