Mathematics Part-II

Book: Mathematics Part-II

Chapter: 9. Differential Equations

Subject: Maths - Class 12th

Q. No. 1 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.

(x2 + xy)dy = (x2 + y2)dx

Here, putting x = kx and y = ky

= k0.f(x,y)

Therefore, the given differential equation is homogeneous.

(x2 + xy)dy = (x2 + y2)dx

To solve it we make the substitution.

y = vx

Differentiating eq. with respect to x, we get

Integrating on both side,

- v - 2log|1 - v| = log|x| + logc

The required solution of the differential equation.


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