A particular solution of $\log(dy/dx)=3x

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Differential Equations

Question:

A particular solution of $\log(dy/dx)=3x+4y,y(0)=0$ is:

Options:

$e^{3x}+3e^{-4y}=4$

$4e^{3x}-3e^{-4y}=3$

$3e^{3x}+4e^{4y}=7$

$4e^{3x}+3e^{-4y}=7$

Correct Answer:

$4e^{3x}+3e^{-4y}=7$

Explanation:

$\frac{dy}{dx}=e^{3x+4y}⇒e^{-4y}dy=e^{3xdx}⇒\frac{e^{-4y}}{-4}=\frac{e^{3x}}{3}+x;y(0)=0⇒c=-7/12$

$⇒3e^{-4y}=-4e^{3x}+7$