1.

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

Answer» Correct Answer - `4e^(3x)+3e^(-4y)=7`
`(dy)/(dx)=e^(3x+4y)=e^(3x)*e^(4y) rArr int e^(3x)dx = int e^(-4y)dy`
`therefore (e^(3x))/(3)=(e^(-4y))/(-4)+C. " " `...(i)
Putting x = 0 and y = 0 in (i), we get `C=((1)/(3)+(1)/(4))=(7)/(12).`
`therefore (e^(3x))/(3)=(e^(-4y))/(-4)+(7)/(12) rArr 4e^(3x)+3e^(-4y)=7.`


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