Mathematics Part-II

Book: Mathematics Part-II

Chapter: 9. Differential Equations

Subject: Maths - Class 12th

Q. No. 3 of Exercise 9.5

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In each of the question, show that the given differential equation is homogeneous and solve each of them.

(x – y)dy – (x + y)dx = 0

(x - y)dy = (x + y)dx

Here, putting x = kx and y = ky

= k0.f(x,y)

Therefore, the given differential equation is homogeneous.

(x - y)dy – (x + y)dx = 0

To make it we make the substitution.

y = vx

Differentiating eq. with respect to x, we get

Integrating both sides we get,

2vdv = dt

The required solution of the differential equation.


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