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  3. 1 state the order of the de and tell whether...

Question: 1 state the order of the de and tell whether...

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1. State the order of the DE and tell whether it is linear or nonlinear. dQ k e. dt Show that y : С1e3x + Схезis a solution for the DE: 3. y Cicos(x) Czsin(x) is a two parameter family of solutions of the DE: y+ y O. Find a general solution that satisfies the initial conditions: yx/4) 2, Y(a/4) 1 YC is a one parameter family of solutions of the DE: y 2xý 4 Find a general solution of the DE that satisfies the initial condition: y(2)- 3. a) Determine whether Theorem 1.1 guarantees that the differential equation dx Vy -4 has a unique solution through the point (1, 3). b) What is the region that is guaranteed by the Theorem 5. 6. Determine a region of the xy- plane for which the given differential equation has a unique solution passing (xo. Yo) in that region. 7. Find the values for m for which y s e is a solution of y-3y. 2y 0 Write down a first order differential equation for the current in an LR-circuit to which a voltage of 100sin(t) is applied in which the inductance is 0.3 henry, resistor is 30 ohms and the initial current is zero. 8.

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