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Question
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`
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`
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