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Geometrical Applications of Differential Equations

We use differential equations for finding the family of curves for which some conditions involving the derivatives are given. For this we proceed in the following way:
Equation of the tangent at a point (x, y) to the curve y = f(x) is given by 102032.png.
At the x-axis, Y = 0, and X = x102026.png (intercept on the x-axis)
At the y-axis, X = 0, and Y = yx 102020.png (intercept on the y-axis)
Similar information can be obtained for normals by writing its equation as 102013.png.

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