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3 Cards in this Set
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What form does the DE need to be for it to be linear? How do we solve FOLDE? |
It must be in the form y'+p(t)y=q(t) We use the coefficient μ=e^∫p(t)dt. Our setup will always look like: μ*y(t)=∫g(t)μdt Then we isolate the y. DO NOT FORGET TO INCLUDE CONSTANT, CONSTANT ALSO GETS DIVIDED BY μ WHEN ISOLATING Y. |
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When is a FODE homogenous? How do we solve a Hom. FODE? |
A FODE is homogenous when every term is of the same degree. (so like x², y², and xy all have the sane degree). If they all are of degree n, we divide each term by 1/xⁿ. We make the substitution v=y/x. Also, substitute dy/dx = v + x(dv/dx). We now have separable DE. once we integrate and have just v, we substitute back in. |
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How can we identify an exact DE? How do we test if a function is an exact homogenous eqn? How do we solve a homogenous eqn? |
Should be in form: M(x,y) + N(x,y)y' Verify that dM/dy = dN/dx Then we integrate M with respect to x, get part of function f(x,y) and tack on a h(y). We know d/dy[f(x,y) + h(y)] = N(x,y) so we end up with terms and h'(y), isolate h'(y) and integrate. plug newly found h(y) back into f(x,y) and done. |
