Solve the following initial value problem: `(dy)/(dx)=y \ tan2x ,\ y(0)=2`

Explanation

``
`frac{d y}{d x}={y} tan 2 {x} `

`Rightarrow frac{d y}{d x} tan 2 {xdx}`

``
This is a variable type

`therefore int frac{d y}{y}=int tan 2 x d x Rightarrow log y=frac{1}{2} log |sec 2 x|+c`

Given `y(0)=2 Rightarrow log 2=frac{1}{2} log |sec 0|+c Rightarrow c=log 2`

`log y=frac{1}{2} log |sec 2 x|+log 2 Rightarrow`

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