#### 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`

Is there an error in this question or solution?

#### APPEARS IN

Solution Solve the Differential Equation `Sin^1 (Dy/Dx) = X + Y` Concept: Solutions of Linear Differential Equation.