Flashcards
DE 1
Flashcards do conjunto (6)
- 1What are the steps to solving Bernoulli Equations1. Isolate dx/dy and compare with general form dy/dx +p(x)y=f(x)y^n
2. substitute into W form
: dw/dx+(1-n)p(x)w=(1-n)*f(x)y
3. find new p(x)
4.find integrating factor
5. multiply the result from step 2 by the integrating factor.
6.integrate the integrating factor* (w)
7.Divide by integrating constant
8.substitute into y-form [w=y^1-n] - 2What are the steps to solve linear 1st order Diff eqs1. Isolate dy/dx & compare with general form
2. Find integrating factor
3. Multiply by O.G. E.Q. by integrating factor.
4. Integrate by integrating factor*(y).
5. Divide by integrating factor - 3What are the steps to solve for orthogonal trajectories1. Find dy/dx
2. Get rid of c1
3. Find the negative reciprocal
4. Separate and solve - 4What are the steps to find a member of a family that satisfies the given initial conditions1. plug in initial conditions into the equation.
2. Add the results together and find c1
3. plug c1 into one of the initial results and find c2
4. plug c1 & c2 into original equation. - 5How do you determine whether the given functions are linearly dependent or independent.Using the wronskian method: when the answer from the determinant is not 0 then the function is linearly independent, and will be dependent if the answer is zero
- 6How do you verify that the given functions form a fund. set of solutions of the D.E. on the indicated interval1. Derive the functions as needed to plug into the EQ
2.Make sure for that the given equation equal zero when the functions are plugged in.
3. Then perform wronskian to prove independence.
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- FlashCards sobre DE 1, criado por Abe Moore em 28-10-2015.
- Criado por
- Abe Moore
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