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22. Differential Equations
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Q13 of 462 Page 22

Show that the differential equation of which is a solution, is


On differentiating with respect to x we have,



Now,




= 4x3


Which is the given equation.


Hence, is solution to the given differential equation.


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11

Assume that a raindrop evaporates at a rate proportional to its surface area. Form a differential equation involving the rate of change of the radius of the raindrop.

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Find the differential equation of all the parabolas with latus rectum ‘4a' and whose axes are parallel to the x - axis.

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Form the differential equation having y = (sin–1 x)2 + A cos–1 x + B, where A and B are arbitrary constants, as its general solution.

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Form the differential equation of the family of curves represented by the equation (a being the parameter):

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Questions · 462
22. Differential Equations
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