# Calculus

posted by .

Consider the differential equation,
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.

• Calculus -

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

• Calculus - note -

3^3/3 = C
C = 9

• Calculus -

Steve is correct.

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