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University of Maryland Baltimore County Differential Equations Questions

University of Maryland Baltimore County Differential Equations Questions

Question Description

I’m working on a differential equations test / quiz prep and need support to help me study.

1. Solve the initial value problem y00 ? 6y0 + 9y = 0 with y(0) = 0, y0(0) = 2.2. Find the general solution of y00 + 6y0 + 13y = 0.3. The techniques and theory we have developed in Chapter 3 are naturally extended to higher orderLHCC differential equations. Extend the methodology of Chapter 3 to find the general solution of2y000 ? 4y00 ? 2y0 + 4y = 0.4. y1 = t2and y2 =1tare solutions of the differential equation t2y00 ? 2y = 0 for t > 0. Use theWronskian to determine if these two solutions can be used as a fundamental set of solutions for thisdifferential equation.5. Create your own second order LHCC differential equation such that as t ? ?, the solutions growwithout bound for some choices of initial conditions, but the solutions approach zero for other choicesof initial conditions. Please clearly state your differential equation AND its general solution.6. Consider a general second order LHCC differential equation ay00 + by0 + cy = 0.a) Show that if a > 0, b > 0, and c > 0, then limt??y = 0 for all solutions y of this differentialequation.b) If a > 0, b > 0, but c = 0, find the general solution of the resulting differential equation. Inaddition, compute limt??y for solutions of the differential equation.7. Consider the non-homogeneous differential equation y00 ? 3y0 ? 4y = g(t). For each g(t) givenbelow, state the appropriate choice of form for yp that you would use to implement the method ofundetermined coefficients. You do NOT need to solve for the coefficients in your yp; you do NOTneed to state the solution of the original differential equation.a) g(t) = ?e?t + e?tcos(t)b) g(t) = 2te4t + e3t8. Use variation of parameters to find the general solution of the differential equation y00+3y0?10y = ektwhere k is an arbitrary constant.

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