Solve the differential equation `4x(dy)/(dx)=5y`, given that `y(1)=3`.

Explanation

`4x(dy)/(dx)=5y`
`implies (4)/(y)dy=(5)/(x)dx`
`implies 4int(1)/(y)dy=5int(1)/(x)dx+logc`
`implies 4logy=5logx+logc`
`implies y^(4)=c*x^(5)`………….`(1)`
Given that at `x=1`, `y=3`
`:. 3^(4)=c*1^(5)impliesc=81`
`:.` From eq. `(1)`
`y^(4)=81*-x^(5)`.