`y' - y = 16`
To solve, rewrite the derivative as `dy/dx` .
`(dy)/dx - y = 16`
Then, express the equation in the form `N(y)dy = M(x) dx` .
`(dy)/dx = y+16`
`(dy)/(y+16) = dx`
Take the integral of both sides.
`int (dy)/(y+16) = int dx`
For the left side of the equation, apply the formula `int (du)/u = ln|u|+C` .
And for the right side, apply the formula `int adx =ax + C`.
`ln |y+ 16| + C_1 = x + C_2`
Then, isolate the y. To do so, move the C1 to the right side.
`ln|y+16| = x + C_2-C_1`
Since C1 and C2 represent any number, express it as a single constant C.
`ln|y+16| = x + C`
Then, convert this to exponential equation.
And, move the 16 to the right side.
`y = e^(x+C) - 16`
Therefore, the general solution is `y = e^(x+C)-16` .