Consider the differential equation,

Question

dy/dx=(x+1)/y^2

with the initial condition y(0)=3.

Write down the particular solution, and hence, calculate the value of y when x=8.7, to 3 dec places.

Answer 1

That can be solved by separation of variables.
y^2 dy = (x+1) dx

y^3/3 = x^2/2 + x + C

If y(0) = 3, then C = 3

y^3/3 = x^2/2 + x + 3

Answer 2

3^3/3 = C
C = 9

Answer 3

Steve is correct.