Solve the differential equation (1 + x^2)dy/dx = x tan(y)

^{Firstly rearrange the equation so that only dy/dx is on the left hand sidedy/dx = (x/(1+x^2)) tan(y)Now separate the variables such that the x terms are on one side with the dx, and the y terms are on the other side with the dy. Now we can place integral signs on both sides.}∫ 1/tan(y) dy = ∫ (x/(1+x^2)) dx
Now use the identity cot(y) = 1/tan(y)
∫ cot(y) dy = ∫ (x/(1+x^2)) dx
Now integrate both sides and remember to include the constant of integration, the '+c'
ln |sin(y)| = (1/2)ln |1+x^2| + c