HW2_math252_sp19.pdf - MATH 252 HW2 due date Feb 25 Monday in class Show your work for all problems You may discuss with classmates or me but write your

# HW2_math252_sp19.pdf - MATH 252 HW2 due date Feb 25 Monday...

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MATH 252 HW2 due date : Feb 25, Monday, in class Show your work for all problems. You may discuss with classmates or me, but write your own answers. No late homework is accepted. 1. Consider the following autonomous differential equation dy dt = y 2 - 4 y + 2 (a) Sketch the phase line and the solution graph. (b) Describe the long-term behavior of the solution when initial condition is the following three cases: y (0) = - 1, y (0) = - 2, and y (0) = 4. 2. Sketch the bifurcation diagram of the following family of autonomous differential equations. #### You've reached the end of your free preview.

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Unformatted text preview: Identify all bifurcation values. (a) dy dt = y 2 + 3 y + a (b) dy dt = y 3 + αy 2 3. Find the general solution to the following differential equations. (a) y = 2 y + 3 e-2 t (b) y =-y + t 3 + sin 3 t (c) y =-y + e t + e-t 4. Solve the given initial value problem using integrating factor. (a) dy dt = 1 t +1 y + 4 t 2 + 4 t, y (1) = 10 (b) dy dt =-2 ty + 4 e-t 2 , y (0) = 3 5. Find the general solution to the following system: dx dt = 2 x, dy dt = 4 y-x 2 . 1...
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