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

If `y=y(x)` is the solution of the differential equation `x(dy)/(dx)+2y=x^(2)` satisfying `y(1)=1`, then `y(1/2)` is equal to `(7k)/16`. The value of k is___________________.

Text Solution

Verified by Experts

The correct Answer is:
7
`(dy)/(dx)+(2/x)y=x`
I.F.`e^(int 2/x dx)=x^(2)impliesyx^(2)=intx xx x^(2) dximpliesyx^(2)=(x^(4))/4+c`
`y(1)=1impliesc=3/4`
Hence `y=1/(4x^(2))(x^(4)+3)impliesy(1/2)=49/16`
Promotional Banner

Similar Questions

Explore conceptually related problems

The solution of the differential equation y(dy)/(dx)=x-1 satisfying y(1) = 1, is

The solution of the differential equation (dy)/(dx) = (x-2y+1)/(2x -4y) is

The solution of the differential equation dy/dx = (1+x)(1+ y^2) is -

The solution of the differential equation (x+2y^(2))(dy)/(dx)=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 (dy)/(dx)=(x+y)/(x) , satisfying the condition y(1)=1 , is