Question

What is the solution of the differential equation  ln(dy/dx) = ax + by?

a. ae^ax + be^by = c

b. 1/ae^ax + 1/b e^by = c

c. ae^ax + be^-by = c

d. 1/ae^ax + 1/be^-by = c

Answer 1

Correct option d. 1/ae^ax + 1/be^-by = c  

Explanation:

dy/dx = e^{(ax + by)} = e^ax x e^by

⇒ e^axdx - e^-bydy = 0

Integrating both sides,

1/ae^ax + 1/b e^-by = c