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Let f(x, y, c1) = 0 and f(x, y, c2) = 0 ...

Let `f(x, y, c_1) = 0 and f(x, y, c_2)` = 0 define two integral curves of homogeneous first order differential equation. If `P_1 and P_2` are respectively the points of intersection of these curves with an arbitrary line, y = mx then prove that the slopes of these two curves at `P_1 and P_2` are equal.

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MOTION-DIFFERENTIAL EQUATION -Exercise 3
  1. (dy)/(dx)=(x+y+1)/(2x+2y+3)

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  2. Show that the curve such that the distance between the origin and the ...

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  3. Let f(x, y, c1) = 0 and f(x, y, c2) = 0 define two integral curves of ...

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  4. Let y=y(t) be a solution to the differential equation y^(prime)+2t ...

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  5. Solution of the differential equation (1-x^(2))(dy)/(dx)+2xy=xsqrt(1-x...

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  6. Solve the following differential equation: (1+y^2)dx=(tan^(-1)y-x)dy

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  7. dy/dx -yln2 = 2^sinx. (cosx-1) ln 2, y being bounded when x rightarrow...

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  8. Consider the differential equation. Dy/dx +P(x)y = Q(x) (i) If two par...

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  9. x(1+y^2)dx-y(1+x^2)dy =0

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  10. Find the integral curve of the differential equation, x(1–x lny). Dy/d...

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  11. A tank consists of 50 litres of fresh water. Two litres of brine each ...

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  12. A normal is drawn at a point P(x , y) of a curve. It meets the x-ax...

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  13. Find the curve for which the sum of the lengths of the tangent and sub...

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  14. Find the curve y= f(x) where f(X) ge 0, f(0) =0,bounding a curvilinear...

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  15. Find the equation of a curve such that the projection of its ordinate ...

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  16. The light rays emanating from a point source situated at origin when r...

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  17. The perpendicular from the origin to the tangent at any point on a cur...

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  18. Find the curve for which any tangent intersects the y-axis at the poin...

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  19. Find the curve such that the area of the trapezium formed by the co-or...

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  20. Find the equation of the curve passing through the origin if the middl...

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