Question

Find the general solution of the differential equation 2y' - y = 0.

a) y = Ce^(0.5x)
b) y = Ce^x
c) y = Ce^(2x)
d) y = Ce^(-0.5x)

Answer 1

To find the general solution of the given differential equation, rearrange the equation by isolating the derivative term, integrate both sides with respect to x, and exponentiate both sides to solve for y.

Step-by-step explanation:

The given differential equation is 2y' - y = 0. We need to find the general solution for this equation.

To solve this, we can rearrange the equation by isolating the derivative term:

2y' = y

Dividing both sides by y, we get:

y'/y = 1/2

Integrating both sides with respect to x gives:

ln|y| = (1/2)x + C

where C is the constant of integration.

Finally, we can exponentiate both sides to solve for y:

y = Ce^x/2

where C is an arbitrary constant.