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17calculus 17calculus
First Order Second Order Laplace Transforms Additional Topics Applications, Practice
Separation of Variables
Linear
Integrating Factors (Linear)
Substitution
Exact Equations
Integrating Factors (Exact)
Linear
Constant Coefficients
Substitution
Reduction of Order
Undetermined Coefficients
Variation of Parameters
Polynomial Coefficients
Cauchy-Euler Equations
Chebyshev Equations
Laplace Transforms
Unit Step Function
Unit Impulse Function
Square Wave
Shifting Theorems
Solve Initial Value Problems
Classify Differential Equations
Fourier Series
Slope Fields
Wronskian
Existence and Uniqueness
Boundary Value Problems
Euler's Method
Inhomogeneous ODE's
Resonance
Partial Differential Equations
Linear Systems
Exponential Growth/Decay
Population Dynamics
Projectile Motion
Chemical Concentration
Fluids (Mixing)
Practice Problems
Practice Exam List
Exam A1
Exam A3
Exam B2

You CAN Ace Differential Equations

17calculus > differential equations > exam A3

Topics You Need To Understand For This Page

Differential Equations Alpha List

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Differential Equations - Exam A3

This page contains a complete differential equations exam with worked out solutions to all problems.

Exam Details

Tools

Time

1 hour

Calculators

no

Questions

7

Formula Sheet(s)

none

Total Points

100

Other Tools

none

Instructions:
- This exam is in three main parts, labeled sections 1-3, with different instructions for each section.
- Show all your work.
- For each problem, correct answers are worth 1 point. The remaining points are earned by showing calculations and giving reasoning that justify your conclusions.
- Correct notation counts (i.e. points will be taken off for incorrect notation).
- Give exact answers.

Section 1

Find the general solution for each of the following differential equations. Each question in this section is worth 5 points.

Question 1

\( y^{(3)}-4y' = 0 \)

answer

solution

Question 2

\( y^{(4)} + 2y''+y=0 \)

answer

solution

Question 3

\( y^{(3)}-3y''+3y'-y = 0 \)

answer

solution

Section 2

Find the general solution for each of the following differential equations. Use the method of undetermined coefficients to find the particular solutions. Each question in this section is worth 15 points.

Question 4

\( y^{(3)} -4y' = 4e^{2t} \)

answer

solution

Question 5

\( y^{(3)}-4y' = 5\cos(t) \)

answer

solution

Section 3

Solve the following problems.

Question 6

[15 points] Solve the initial value problem \( y^{(4)} + 13y''+36y = 0; ~~~ y(0)=5, y'(0)=y''(0) = y^{(3)}= 0 \)

answer

solution

Question 7

[40 points] Find the general solution and use the method of variation of parameters to find the particular solution for \( y^{(3)} - 3y''+3y'-y=6e^t \).

answer

solution

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