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Show that the family of curves for which...

Show that the family of curves for which the slope of the tangent at any point (x, y) on it is `(x^(2)+y^(2))/(2xy)`, is given by `x^(2)-y^(2)= Cx`.

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ARIHANT PUBLICATION-DIFFERENTIAL EQUATION-CHAPTER PRACTICE (LONG ANSWER TYPE QUESTIONS)
  1. Form the differential equation of the family of circles in the second ...

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  2. Show that the differential equation represents the family of all parab...

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  3. Solve the differential equation (dy)/(dx)=(e^(x)(sin^(2)x+sin 2x))/(y(...

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  4. Solve the differential equation (dy)/(dx)=1+x+y^(2)+xy^(2), when y=0, ...

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

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  6. Show that the differential equation (x^(2)+xy)dy=(x^(2)+y^(2))dx is ho...

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

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  8. Show that the differential equation (x^(2)-y^(2))dx+2xydy=0 is homogen...

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  9. Solve the differential equation (1+e^(x))dx+(1+e^(y))dy=0.

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  10. Find the particular solution of the differential equation 2xy+y^(2)-2x...

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  11. Solve x^(2)(dy)/(dx)-xy=x ,"x=1, y= (pi)/(2).

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  12. Solve the initial value problem (xe^(y/x)+y)dx= x"dy, y(1)=1.

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  13. Show that the family of curves for which the slope of the tangent at a...

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  14. Find the general solution of (dy)/(dx)+3y=1/ e^(3x).

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  15. Solve the differential equation x(dy)/(dx)-ay= x+1.

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  16. Solve y+(d)/(dx)(xy)=x(sin x+ log x).

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  17. Find the particular solution of the differential equation (dy)/(dx)-x=...

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  18. Find the particular solution of the differential equation (dy)/(dx)=(y...

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  19. Find the equation of a curve passing through the origin and satisfying...

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  20. Find the particular solution of the differential equation (1+x^2)(dy)/...

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