Differential Equations 1 Question 9

9. A solution of the differential equation dydx2xdydx+y=0 is

(1999, 2M)

(a) y=2

(b) y=2x

(c) y=2x4

(d) y=2x24

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Answer:

Correct Answer: 9. (c)

Solution:

  1. Given differential equation is

dydx2xdydx+y=0

(a) y=2dydx=0

On putting in Eq. (i),

02x(0)+y=0

y=0 which is not satisfied.

(b)

y=2xdydx=2

On putting in Eq. (i),

(2)2x2+y=042x+y=0y=2x which is not satisfied. y=2x4dydx=2

On putting in Eq. (i)

(2)2x2+y42x+2x4=0y=2x4 is satisfied. y=2x24dydx=4x

On putting in Eq. (i),

(4x)2x4x+y=0y=0 which is not satisfied. 



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