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Form the differential equation of family...

Form the differential equation of family of circles having center at origin.

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The correct Answer is:
`x+y(dy)/(dx)=0`

Equation of family of such concentrate circles is given by `x^(2)+y^(2)=r^(2)`.
Differentiating w.r.t. x, we get
`2x+2y(dy)/(dx)=0`
or `x+y(dy)/(dx)=`0, which is required differential equation.
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  13. Solve (x-y)(dx+dy)=dx-dy, given that y=-1, where x=0.

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  14. Solve (dy)/(dx) = yf^(')(x) = f(x) f^(')(x), where f(x) is a given int...

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  15. Solve (dy)/(dx)=cos(x+y)-sin(x+y).

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  16. If a function 'f' satisfies the relation f(x)f^('')(x)-f(x)f^(')(x) -f...

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  17. Solve the following differential equation: \ x(dy)/(dx)-y=2\ sqrt(y^2-...

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  18. Solve [2sqrt(x y)-x]dy+ydx=0

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  19. Solve x(dy)/(dx)=y(logy-logx+1)

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  20. Solve [xsin^2(y/x)-y]dx+x dy=0; y=pi/4 when x=1.

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