APMA 2130 UVA 2.1-2.6 Questions and Answers (100% Correct Answers) Already Graded A+

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APMA 2130 UVA 2.1-2.6 Questions and
Answers (100% Correct Answers) Already
Graded A+
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)
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Solving a first order linear equation Ans: Use the integrating factor.


1. Put the equation in standard form
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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


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

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


2. Find y' in terms of v and x
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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.


5. plug in y/x for v


6. Solve for y


Exponential growth Ans: Where rate of population growth is directly
proportional to population size


Exponential growth (form of differential equation) Ans: y' = ky, where k>0


Exponential decay (form of differential equation) Ans: y' = ky, where k <
0


Coefficient functions Ans: Standard form is y'(t) + p(t)y = g(t)