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- Ana is shaking while receiving her exam paper and surprise after she know that the given equation in exam are related to one she reviewed.
- MIDTERM EXAMINATION INDIFFERENTIAL EQUATION
- Malaki na ang chance kong makapasa dito, related yung equation dun sa nireview ko!
- X HAWK
- 1. Find a solution to the initial-value problem y" + 4y = 0; y (0) = 0, y'(0) = 1, if the general solution to the differential equation is known to be y(x) = C1sin 2x + C2cos
- MIDTERM EXAMINATION INDIFFERENTIAL EQUATION
- Ana is now taking her exam with confident as she discusses in her mind the process on how to solve the Particular solution for the given equation.
- X HAWK
- Basic to Particular solution lang
- MIDTERM EXAMINATION INDIFFERENTIAL EQUATION
- Since y(x) is a solution of the differential equation for all values of C1 and C2, I seek those values of C1 and C2 that will also satisfy the initial conditions. Note that y (0) = C1 sin 0 + C2 cos 0 = C2. To satisfy the first initial condition. y (0) = 0, I will choose C2 = 0
- X HAWK
- Furthermore. y'(x) = 2C1 cos 2x — 2C2 sin 2x; thus, y'(0) = 2 C1cos 0 — 2 C2sin 0 = 2 C1. To satisfy the second initial condition; y'(0) = 1, I choose 2 C1, = 1, or C1 = 1/2. Substituting these values of C1 and C2 into y(x), I obtain y(x) = 1/2sin 2x as the solution of the initial-value problem
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