Question

DIFFERENTIAL EQUATIONS
Solve the differential equations.
dy = 4 − x
/
dx

Answer 1

We have dy/dx = (4-x) dx which is a first order linear ODE

dy = (4-x) dx. Now integrating both sides we get:

y = 4x - 1/2 x^2 + C

which is the answer. Note we only wrote +c once since we can combine arbitrary constants under addition and subtraction with each other.

Answer 2

anti derivative of 4 is 4x
anti derivative of -x is -1/2 x^2

so y = 4x - (1/2)x^2 + C
(can't forget constants when doing anti derivatives xD)

is this what you need?

*edit
Anti-derivative of a Constant [just a number] becomes (constant)*x
for example integral of 5 = 5x + C

Then there is a Power Rule for integrals
integral of (x)^n = 1/(n+1) *(x)^(n+1) + C
for example: integral of x^2 = 1/(2+1) * (x)^(2+1) + C = (1/3)*x^3 + C