Answer
$1.5574$
Work Step by Step
In order to determine the exact solution, isolate the x and y terms on one side and integrate both sides.
$\int \dfrac{dy}{1+y^2}=\int dx$ ...(1)
In order to determine the differential equation, we will have to take the derivative of the differential equation.
Equation (2) gives: $\arctan (y)=x+c$ ...(2)
Apply the initial conditions, to calculate the value of $c$
$\arctan (0)=0+c\implies c=0$
Now, the particular solution is as follows:
$\arctan (y)=x$ or, $y=\tan x$
Thus, the exact solution is: $y(1)=\tan (1) \approx 1.5574$
