Maharashtra State BoardHSC Arts 12th Board Exam
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The differential equation of y=c/x+c^2 is - Mathematics and Statistics

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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`

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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`

Concept: General and Particular Solutions of a Differential Equation
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