Solving Differential Equations (Leaving Cert Applied Maths): Quizzes

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Solving Differential Equations
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What makes an equation a differential equation?

It contains derivatives

What is the highest derivative in a 1st order differential equation?

dydx\frac{dy}{dx}

What is the highest derivative in a 2nd order differential equation?

d2ydx2\frac{d^2y}{dx^2}

How many types of differential equations are in the Leaving Cert Applied Maths course?

Three

What characterises a general solution?

Contains arbitrary constant cc

What is the first step in solving Type 1 differential equations?

Separate the variables

What distinguishes Type 2 from Type 1 differential equations?

Type 2 has initial conditions given

What substitution is used for Type 3 (2nd order) differential equations?

Let v=dydxv = \frac{dy}{dx}

What does variable separation achieve?

All yy terms one side, xx terms other

When are initial conditions used to find the constant cc?

For particular solutions

What must always be included when integrating?

Constant of integration cc

What is ∫1ydy\int \frac{1}{y} dy equal to?

ln⁡y+c\ln y + c

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