Grade 12 Differential Equations Worksheet
A comprehensive worksheet for Grade 12 students covering various aspects of differential equations, including solving techniques, initial value problems, and applications.
Includes
Standards
Differential Equations: Grade 12
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Read each question carefully and show all your work. Simplify your answers where possible.
1. Solve the following first-order linear differential equation: dy/dx + 2xy = e^(-x^2).
2. A differential equation is called if it can be written in the form dy/dx = f(y/x).
3. To solve a homogeneous differential equation, we typically use the substitution y = .
4. Given the initial value problem dy/dx = 3x^2, y(0) = 2, what is the particular solution?
y = x^3
y = x^3 + 2
y = x^3 + C
y = x^3 - 2
5. A differential equation of the form dy/dx = f(x)g(y) is called separable.
True
False
6. A quantity y is proportional to its rate of change. Write a differential equation that represents this relationship and solve it.
Match each term on the left with its definition on the right.
7. General Solution
a. A solution to a differential equation that satisfies a given initial condition.
8. Particular Solution
b. A solution containing arbitrary constants.
9. Integrating Factor
c. A function used to solve first-order linear differential equations.