Differential Equations Answers

solve the given equations using exact differential

equations.

6. (cos x ∙ cos y − cot x)dx − (sin x ∙ sin y)dy = 0

7. x(3xy − 4y3 + 6)dx + (x3 − 6x2y2 − 1)dy = 0, when x = 2, y = 0

8. 2xydx + (y2 + x2)dy = 0

9. (xy2 + y − x)dx + x(xy + 1)dy = 0, when x = 1, y = 1

|10. (1 − xy)−2dx + [y2 + x2(1 − xy)−2]dy = 0, when x = 3, y = 4

solve the given equations using exact differential

equations.

1. (6x + y2)dx + y(2x − 3y)dy = 0

2. (y2 − 2xy + 6x)dx − (x2 − 2xy + 2)dy = 0, when x = 1, y = 2

3. v(2uv2 − 3)du + (3u2v2 − 3u + 4v)dv = 0, when u = 1, v = 1

4. (1 + y2 + xy2)dx + (x2y + y + 2xy)dy = 0

5. (w3 + wz2 − z)dw + (z3 + w2z − w)dz = 0, when w = 4, z = 2

In an R-L-C series circuit, the differential equation for the instantaneous charge q(t) on the capacitor is   2 2   d q dq q L R Et dt dt C . Determine the charge q(t) and current i(t) for a circuit with R  10 ohm, L = 1 henry, C = 2 10 farad and E(t) = 50 10 cos t volts. What is the steady-state current for this circuit?

Given that p(x) = x is a particular solution to the

differential equation y''+ y = x write the generalized sotlution and check by verifying that the solution satisfies

the equation

Find the general solution to

y'' − y'− 2y = 2e^3x