Particular Solutions (Edexcel A-Level Mathematics): Flashcards

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Particular Solutions
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Define a differential equation in mathematics.

An equation that relates a function to its derivatives.

What is the goal of solving a differential equation?

Find a function that satisfies the equation.

What indicates a general solution in DE?

It contains a constant, usually denoted by +c+c.

What defines a particular solution of a differential equation?

It includes specific values for the constants involved.

Example equation of a curve from dydx\frac{dy}{dx}?

y=x3+ax+cy = x^3 + ax + c, using integration.

What is the method of separating variables?

Organizing dxdx and dydy on opposite sides.

What is the solution to ln⁡∣y∣=k\ln|y| = k?

y=±eky = \pm e^k, where kk is a constant.

What is the max height of a shrub modeled by DE?

6 meters, as hh approaches 6.

Write the differential equation for water flow.

dx/dt=−k∗sqrt(x)dx/dt = -k * sqrt(x), where kk is a proportional constant.

Find tt when x=0.5x = 0.5 in the water tank model equation.

t≈8.5t \approx 8.5 minutes from the tank model equation result.

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