Find the particular solution of the differential equation log(dy/dx)= 3x + 4y, given that y = 0 when x = 0. - Mathematics

Find the particular solution of the differential equation log(dy/dx)= 3x + 4y, given that y = 0 when x = 0.

Solution

Consider the differential equation,

log(dy/dx)=3x+4y

Taking exponent on both the sides, we have

e^log(dy/dx)=e^(3x+4y)

=>dy/dx=e^(3x+4y)

=>dy/dx=e^(3x).e^(4y)

=>dy/(e^(4y))=e^(3x)dx

Integration in both the sides, we have

intdy/e^4y=inte^(3x)dx

e^(-4y)/(-4)=e^(3x)/3+C

We need to find the particular solution.

We have, y=0, when x=0

1/(-4)=1/3+C

=>C=-1/4-1/3

=>C=(-3-4)/12=-7/12

Thus, the solution is e^(3x)/3+e^(-4y)/4=7/12

Concept: General and Particular Solutions of a Differential Equation
Is there an error in this question or solution?