APMA 2130 UVA 2.1-2.6 Questions and Correct Answers

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APMA 2130 UVA 2.1-2.6 Questions and
Correct Answers
first order linear equation (form) Ans: P(t)y' + Q(t)y = G(t)

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

Solving a first order linear equation Ans: 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) Ans: M(y)y'(x) = N(x)

Solving a separable equation Ans: 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) Ans: y' = f(x,y), where f(x,y) can be
written as g(v), where v = y/x

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




2. Find y' in terms of v and x




3. Substitute in y' and y, in terms of v and x




4. You should get a separable equation, in terms of v and x. Solve
for v.



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