Home
Class 12
MATHS
If y = y(x) is the solution of the diff...

If `y = y(x)` is the solution of the differential equation,`x (dy)/(dx) + 5y = 10x^5, x > 0` satisfying `y(1) = 2` then range of `y(x)` for `x > 0` is:

A

`[1,oo)`

B

`[2 , oo)`

C

`(2, oo)`

D

`[4,00)`

Text Solution

Verified by Experts

The correct Answer is:
B
`(dy)/(dx) + (5y)/(x) = 10x^(4) , x > 0`
I.F. `e^(5int1/x dx) = x^5`
Solution is given by `y cdot x^5 = 10 int x^9 dx + c = x^(10) + c`
`y = x^5 + c/(x^5) = y(x)`
At `x = 1, y = 2 implies c = 1`
`y = x^5 + 1/(x^5) in [2, oo)" "("Using" AM ge GM)`.
Promotional Banner

Similar Questions

Explore conceptually related problems

Solution of the differential equation (x+a)(dy)/(dx)-3y=(x+a)^(5) is

The solution of the differential x(x-y) (dy)/(dx) = y(x+y) , is

The solution of the differential equation x(dy)/(dx) + 2y = x^2 (X ne 0) with y(1) =1, is :

Solution of the differential equation y dx+(x-y^(2))dy=0 is

Solution of the differential equation (1+x)y dx+(1-y)x dy=0 is

(5) The solution of the differential equation (y-xy^(2))dx-(x+x^(2)y)dy=0

The solution of the differential equation (dy)/(dx)=(x-y+3)/(2x(x-y)+5) is