Find the particular solution If dydx 5x2 2 and y 3 30 ySo

Solution

Find the particular solution If dy/dx = 5x^2 - 2 and y (3) = 30; y=

dy = (5x^2-2) dx

take integration thus

y = 5x^3/3 - 2x + C

y = 30 = 5 *9 - 2*3 +C

30 = 45-6 +C

C = 30 - 39 = -9

y = 5x^3/3 - 2x - 9