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Question
Solve the differential equation `sin^(-1) (dy/dx) = x + y`
Solution
Put x + y = t
`1 + dy/dx = dt/dx`
`dy/dx = dt/dx - 1`
Now, `dy/dx = sin (x + y)`
`dt/dx - 1 = sin t`
`dt/dx = 1 + sin t`
`int dt/(1+ sint) = int dx`
`int (1 -sint)/(1-sin^2 t)dt = x + c`
`int (1- sint)/cos^2t dt = x + c`
`int sec^2 t dt - int tant sec t dt = x + c`
`tan t - sect = x + c`
`tan(x + y) - sec(x + y) = x + c`
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