The tangent at any point `(x , y)` of a curve makes an angle `tan^(-1)(2x+3y)` with x-axis. Find the equation of the curve if it passes through (1,2).

Explanation

The slope of the curve is given as `frac{d y}{d x}=tan theta` Here,


`theta=tan ^{-1}(2 x+3 y) `

`therefore frac{d y}{d x}=tan (tan ^{-1} 2 x+3 y) `

`Rightarrow frac{d y}{d x}=2 x+3 y `

`Rightarrow frac{d y}{d x}-3 y=2 x ldots .(1)`

Clearly, it is a linear differential equation of the form


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