Answer:
[tex]y(x)=4x^2 -3x -10[/tex]
Step-by-step explanation:
First take the integral of dy/dx to find a general formula for y(x):
[tex]\frac{dy}{dx} =8x-3\\y(x) = \int{(8x-3)} \, dx =4x^2 -3x +c[/tex]
Then, evaluate the expression found above at y(2)=0 in order to find the value for the constant 'c':
[tex]y(x) = 4x^2 -3x +c\\y(2) = 0\\0= 4*(2)^2 -(3*2) +c\\c=6-16 = -10[/tex]
The expression for y(x) that satisfies both conditions is:
[tex]y(x)=4x^2 -3x -10[/tex]
