Question

The function y = Cx + 3 is the general solution of

a)y"= 0
b)xy' -y + 6 = 0
c)y" + y-3 = 0
d)y'-y + 3 = 0
e)y' - xy + 3 = 0
f)None of the above.

Answer 1

The function y = Cx + 3 is the general solution to the differential equation xy' - y + 6 = 0, which makes b) the correct answer.

Step-by-step explanation:

This is because the given function y = Cx + 3 is a first-order linear homogeneous equation.

To find which differential equation the function y = Cx + 3 is a general solution to, we need to perform differentiation and then substitute into the provided differential equations to check for validity. Differentiating y = Cx + 3 with respect to x gives us the first derivative y' = C.

The given function is y = Cx + 3. This equation is a linear function because the highest power of x is 1. It represents a straight line when graphed. The constant term 3 represents the y-intercept, which is the value of y when x is equal to 0.