Form a differential equation of the family of the curves $y^2 = 4ax$.
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Differential Equations - ISC Class 12 Mathematics Questions with Answers, Page 3
50 past-paper questions on Differential Equations from ISC Class 12 Mathematics papers (2027-2017), newest first, in full. Questions 41-50 are on this page, 20 to a page. Tap "Show answer" under a question to see its answer.
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Solve the differential equation $(1 + x^2)\frac{dy}{dx} = 4x^2 - 2xy$.
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Solve the differential equation:
$\frac{dy}{dx} = \frac{x + y + 2}{2(x + y) - 1}$
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Solve: $\sin x \frac{dy}{dx} - y = \sin x \tan\frac{x}{2}$.
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Solve the following differential equation:
$x \frac{dy}{dx} + 2y = x^2 \log x$
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Find the differential equation of the family of concentric circles $x^2 + y^2 = a^2$.
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Find the differential equation of the family of curves $y = Ae^x + Be^{-x}$, where $A$ and $B$ are arbitrary constants.
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The population of a town grows at the rate of $10\%$ per year. Using differential equation, find how long will it take for the population to grow $4$ times.
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Solve:
$\frac{dy}{dx} = 1 - xy + y - x$
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Solve: $(x^2 - yx^2) \, dy + (y^2 + xy^2) \, dx = 0$
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