Question

Find the function y(x) satisfying dy/dx=8x-3 and y(2)=0y(x)=?

Answer 1

`y(x)=4x^2 -3x -10`

Explanation:

First take the integral of dy/dx to find a general formula for y(x):

`(dy)/(dx) =8x-3\\y(x) = \int{(8x-3)} \, dx =4x^2 -3x +c`

Then, evaluate the expression found above at y(2)=0 in order to find the value for the constant 'c':

`y(x) = 4x^2 -3x +c\\y(2) = 0\\0= 4*(2)^2 -(3*2) +c\\c=6-16 = -10`

The expression for y(x) that satisfies both conditions is:

`y(x)=4x^2 -3x -10`