#### 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`

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#### Solution

**(a)**

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

Differentiating w.r.t.x,

`dy/dx=c/x^2...........(ii)`

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

`(dy/dx)^2=c^2/x^4`

`x^4(dy/dx)^2=c^2`

`x^4(dy/dx)^2=y-c/x ["From " (i)]`

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

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

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#### Reference Material

Solution for question: The differential equation of y=c/x+c^2 is concept: General and Particular Solutions of a Differential Equation. For the courses HSC Science (Electronics), HSC Science (Computer Science), HSC Science (General) , HSC Arts