Question

How to you find the general solution of `dy/dx=5e^(-x/2)`?

Answer 1

THe general solution is `y=-10e^(-x/2)+C`

Explanation:

`dy/dx=5e^(-x/2)`
`:. dy=5e^(-x/2)dx`
Integrating both sides
`intdy=5inte^(-x/2)dx`
We use the substitution, `u=-x/2` `=>` `-2du=dx`
`y=5int-2e^(u)du=-10e^(u)=-10e^(-x/2)+C`