# Lesson Worksheet: Linear Homogeneous Differential Equations with Constant Coefficients Mathematics

In this worksheet, we will practice solving second- and higher-order linear homogeneous differential equations with constant coefficients.

Q1:

Suppose there are differentiable functions and , defined for all real numbers and satisfying and .

From the derivatives, what can you deduce about ?

• A is a constant function.
• B is an exponential function.
• C is a hyperbolic function.
• D always equals 0.
• E is a trigonometric function.

It is known that every function that satisfies is a combination for some constants and . Find all functions satisfying and , where .

• A and
• B and
• C and
• D and
• E and

Sketching graphs of the functions above suggest that for some constants and . Find these constants, where .

• A,
• B,
• C,
• D,
• E,

Q2:

The functions , , and are three linearly independent solutions of the differential equation . Find a particular solution satisfying the initial conditions , , and .

• A
• B
• C
• D
• E

Q3:

The functions , , and are three linearly independent solutions of the differential equation . Find a particular solution satisfying the initial conditions , , and .

• A
• B
• C
• D
• E

Q4:

The functions , , and are three linearly independent solutions of the differential equation . Find a particular solution satisfying the initial conditions , , and .

• A
• B
• C
• D
• E

Q5:

The functions , , and are three linearly independent solutions of the differential equation . Find a particular solution satisfying the initial conditions , , and .

• A
• B
• C
• D
• E

Q6:

The functions , , and are three linearly independent solutions of the differential equation . Find a particular solution satisfying the initial conditions , , and .

• A
• B
• C
• D
• E

Q7:

The functions , , and are three linearly independent solutions of the differential equation . Find a particular solution satisfying the initial conditions , , and .

• A
• B
• C
• D
• E