Use separation of variables to find the general solution of the differential equation.
A)
B)
C)
D)
E)

Question

​Use separation of variables to find the general solution of the differential equation. ​  ​
A) ​ 
B) ​ 
C) ​ 
D) ​ 
E) ​

Quizplus · Accepted Answer

The differential equation can be written as:
dy/dx = (x^2 + y^2)/(2xy)
Multiplying both sides by 2xy and dividing both sides by y^2:
(2/x)dx + (-2/y)dy/y = 0
Integrating both sides:
2ln|x| – 2ln|y| = c1
ln|x^2/y^2| = c1
Taking the exponential of both sides:
x^2/y^2 = c2
y = ±x/c
Where c is a constant which can take positive or negative values. Therefore, the general solution of the differential equation is y = ±x/c.

​Use Separation of Variables to Find the General Solution of the Differential

Use Separation of Variables to Find the General Solution of the Differential