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

Explanation

Given differential equation can be written as

`\frac{d y}{d x}=e^{(3 x+4 y)}=e^{3 x} \cdot e^{4 y}`
`\int e^{-4 y} d y=\int e^{3 x} d x`
`\frac{e^{-4 y}}{-4}=\frac{e^{3 x}}{3}+C`
`\therefore \quad 4 e^{3 x}+3 e^{-4 y}+12 C=0`
Taking `x=0, y=0`, we get `\therefore=-\frac{7}{12}`

`\therefore` The solution is `4 e^{3 x}+3 e^{-4 y}-7=0`