Solving Technique | MCQs

Explanation

0.5x + 5 = x - 0.75

Solving for x:

1. Move 0.5x to the right side:
   5 = x - 0.75 - 0.5x
2. Simplify:
   5 + 0.75 = x - 0.5x
   5.75 = 0.5x
3. Divide by 0.5:
   x = 11.5

Explanation

The given differential equation is a second-order linear homogeneous equation with constant coefficients. The characteristic equation is:

r^2 - 4r + 4 = 0

which has a repeated root r = 2. Therefore, the general solution is:

y = (c1 + c2x)e^2x

where c1 and c2 are arbitrary constants.