RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 20. Homogeneous Differential Equations

Subject: Maths - Class 12th

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Exercise 20

1

In each of the following differential equation show that it is homogeneous and solve it.

xdy = (x + y)dx
2

In each of the following differential equation show that it is homogeneous and solve it.

(x2 - y2)dx + 2xydy = 0
3

In each of the following differential equation show that it is homogeneous and solve it.

x2dy + y(x + y)dx = 0
4

In each of the following differential equation show that it is homogeneous and solve it.

(x - y)dy - (x + y)dx = 0
5

In each of the following differential equation show that it is homogeneous and solve it.

(x + y)dy + (y - 2x)dx = 0
6

In each of the following differential equation show that it is homogeneous and solve it.

(x2 + 3xy + y2)dx - x2dy = 0
7

In each of the following differential equation show that it is homogeneous and solve it.

2xydx + (x2 + 2y2)dy = 0
8

In each of the following differential equation show that it is homogeneous and solve it.
9

In each of the following differential equation show that it is homogeneous and solve it.
10

In each of the following differential equation show that it is homogeneous and solve it.
11

In each of the following differential equation show that it is homogeneous and solve it.
12

In each of the following differential equation show that it is homogeneous and solve it.
13

In each of the following differential equation show that it is homogeneous and solve it.

x2 = x2 + xy + y2
14

In each of the following differential equation show that it is homogeneous and solve it.
15

In each of the following differential equation show that it is homogeneous and solve it.
16

In each of the following differential equation show that it is homogeneous and solve it.
17

In each of the following differential equation show that it is homogeneous and solve it.

(x - y) = x + 3y
18

In each of the following differential equation show that it is homogeneous and solve it.

(x3 + 3xy2)dx + (y3 + 3x2y)dy = 0
19

In each of the following differential equation show that it is homogeneous and solve it.

dy = ydx
20

In each of the following differential equation show that it is homogeneous and solve it.

x2 + y2 = xy
21

In each of the following differential equation show that it is homogeneous and solve it.

(log y - log x + 1)
22

In each of the following differential equation show that it is homogeneous and solve it.

x–y + xsin = 0
23

In each of the following differential equation show that it is homogeneous and solve it.

x = y - xcos2
24

In each of the following differential equation show that it is homogeneous and solve it.
25

Find the particular solution of the different equation.2xy + y2 - 2x2 = 0, it being given that y = 2 when x = 1
26

Find the particular solution of the differential equation dx + xdy = 0, it being given that y = when x = 1.
27

Find the particular solution of the differential equation given that y = 1 when x = 1.
28

Find the particular solution of the differential equation xey/x - y + x = 0, given that y(1) = 0.
29

Find the particular solution of the differential equation xey/x - y + x = 0, given that y(e) = 0.
30

The slope of the tangent to a curve at any point (x,y) on it is given by , where x>0 and y>0. If the curve passes through the point, find the equation of the curve.