Advertisement Remove all ads

The differential equation of y=c/x+c^2 is - Mathematics and Statistics

Sum

The differential equation of `y=c/x+c^2` is :

(a)`x^4(dy/dx)^2-xdy/dx=y`

(b)`(d^2y)/dx^2+xdy/dx+y=0`

(c)`x^3(dy/dx)^2+xdy/dx=y`

(d)`(d^2y)/dx^2+dy/dx-y=0`

Advertisement Remove all ads

Solution

(a)

`y=c/x+c^2..........(i)`

Differentiating w.r.t.x,

`dy/dx =(- c)/x^2 + 0 `

`c = -x^2  "dy"/"dx"`  ..........(2)

Putting in equation (1)

`y = (-"x"^2 "dy"/"dx")/"x" + (-"x"^2  "dy"/"dx")^2`

 

`y = -"x" "dy"/"dx" + "x"^4 ("dy"/"dx")^2`

 

`x^4(dy/dx)^2-xdy/dx=y`

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×