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# Find the particular solution of the differential equation log(dy/dx)= 3x + 4y, given that y = 0 when x = 0. - CBSE (Science) Class 12 - Mathematics

ConceptGeneral and Particular Solutions of a Differential Equation

#### Question

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

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Solution Find the particular solution of the differential equation log(dy/dx)= 3x + 4y, given that y = 0 when x = 0. Concept: General and Particular Solutions of a Differential Equation.
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