Solve the seperable differential equation 8yy�Œ =x. Use the following initial condition: y(8)=4.

Question

Express x^2 in terms of y.

Answer 1

8yy' = x
8y dy = x dx
4y^2 = 1/2 x^2 + c

4(16) = 1/2 (64) + c
c = 32

4y^2 = 1/2 x^2 + 32
8y^2 - x^2 = 64
y^2/8 - x^2/64 = 1