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3 Cards in this Set
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How do we solve nonconstant coefficients SODE? What does that type look like? |
A(t)y'' + B(t)y' + C(t)y = 0 We solve it using the reduction of order method given y₁. This eqn is y₂= vy₁ where v=∫[e^(-∫p(t)dt)]/y₁², so y₂=y₁∫[(e^-∫p(t)dt)]/y₁² |
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When the method of undetermined coefficients does not work, what method do we use? What eqn is it? |
We have a yp =u₁y₁ +u₂y₂, where, u₁ = -∫y₂g(t)/W dt u₂ = ∫y₁g(t)/W dt and thus our final general soln is yg = yh + yp = C₁y₁+C₂y₂ + u₁y₁ + u₂y₂ so its still necessary to find yh. Also do not add more constants for yp, the constants for our general soln are taken care of in yh. |
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