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Form the differential equation of family...

Form the differential equation of family of lines concurrent at the origin.

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Equation of family of line concurrent at origin is given by y=mx
`therefore (dy)/(dx)=m`
Putting the value of m in (1), we get
`y=(dy)/(dx).x`
or `xdy-ydx=0`, which is required differential equation of order q. Here order is same as number of effective constants in the equation of family of curve.
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CENGAGE-DIFFERENTIAL EQUATIONS-Examples
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  8. What is the order of the differential equation whose general solution ...

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  10. Solve log(dy/dx)=4x-2y-2 , given that y=1 when x=1.

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  11. Solve the differential equation x y(dx)/(y dx)=(1+y^2)/(1+x^2)(1+x+x^2...

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  13. Solve (d^2y)/(dx^2)=((dy)/(dx))^2

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  14. Solve (dy)/(dx)=(x+y)^2

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  15. Solve (dy)/(dx) sqrt(1+x+y) =x+y-1

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  16. Show that the given differential equation is homogeneous and solve eac...

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  17. x dy - y dx = sqrt(x^(2) + y^(2)) dx

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  18. Solve xsin(y/x)dy=(ysin(y/x)-x)dx.

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  19. (1 + e^(x)/(y)) dx + e^(x)/(y)(1 - (x)/(y)) dy = 0

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  20. Solve x dy=(y+x(f(y/x))/(f^(prime)(y/x)))dx

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