APMA 2130 UVA 2.1-2.6 Questions with Answers (100% Correct Answers)

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APMA 2130 UVA 2.1-2.6 Questions with Answers (100%
Correct Answers)

first order linear equation (form) Answer: P(t)y' + Q(t)y = G(t)

Standard form of a first order linear equation Answer: y' + p(t)y = g(t)

Solving a first order linear equation Answer: Use the integrating

factor.




1. Put the equation in standard form

2. integrating factor = μ = e^∫p(t)dt

3. Multiply both sides of the equation by the integrating factor

4. d/dt(μy) = μg(t)

5. Integrate both sides

6. Solve for y

Separable equation (form) Answer: M(y)y'(x) = N(x)

Solving a separable equation Answer: 1. Put y' in the form of dy/dx

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2. Multiply both sides by dx, so you get dx on one side and dy on the

other




3. Move stuff around to get it into the form f(x)dx = g(y)dy




4. Integrate both sides




5. Solve

Homogeneous equation (form) Answer: y' = f(x,y), where f(x,y) can be

written as g(v), where v = y/x

Solving a homogeneous equation Answer: 1. Since v = y/x, y = vx




2. Find y' in terms of v and x




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