Use the integration to find the general solution of the differential equation

Question

​Use the integration to find the general solution of the differential equation  ​

Quizplus · Accepted Answer

Using separation of variables:

dy/dx = (x^2 - y^2)/(2xy)

dy/(x^2 - y^2) = dx/(2xy)

Now using partial fractions:

1/2∫(1/x - 1/y)dy + 1/2∫(1/x + 1/y)dx = C1

1/2ln∣x-y/xy∣ + 1/2ln∣x+y/xy∣ = C1

ln∣(x^2 - y^2)/xy∣ = 2C1

So,

(x^2 - y^2)/xy = C2

(x/y)^2 - 1 = C2

(x/y)^2 = C2 + 1

Therefore,

x/y = ±√(C2 + 1)

x = ±y√(C2 + 1)

Therefore, the general solution is y = x/k where k is a constant of integration.

​Use the Integration to Find the General Solution of the Differential