Mathematics Part-II

Book: Mathematics Part-II

Chapter: 9. Differential Equations

Subject: Maths - Class 12th

Q. No. 11 of Exercise 9.5

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11

For each of the differential equations in question, find the particular solution satisfying the given condition:

(x + y)dy + (x – y) dx = 0; y = 1 when x = 1

(x + y)dy + (x - y)dx = 0



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 solve it we make the substitution.


y = vx


Differentiating eq. with respect to x, we get










Integrating both sides, we get






y = 1 when x = 1













The required solution of the differential equation.


12

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