Differential Equations Answers

Question1

The conditions in a certain electrical circuit is represented by the following differential equation:

1/50Q’’ +Q’ +8q =50 Cos30t

1.      Determine an expression for q in term of t

2.      Determine an expression for the current  I        (hint I =dq/dt)

3.      Determine the amplitude and the frequency of the steady state current.

Question2

Find the general solution of the following DE using the method of undetermined coefficients :

Y’’ +2y’+5y = 34sinxcosx  

Find the surface whose tangent plane cut off an intercept of constant length k from the axis z

Eliminate arbitrary constants from z=(x-a)²+(y-b)² to form the partial differential equation.

d^2u/dx^2 - d^2u/dy^2 = 2(e^(-x)) + 3sin2y

p-3q = sinx+cosy

y"(t) + 4y'(t) + 4y(t) = 4e^-2t, y(0) = -1, y'(0) = 4

Solve for x and y in the following set of simultaneous differential equations by using D-operator methods: (D-2)x + Dy = 10sin2t

Dx + (D+2)y = 0

Show that f(x y)=xy^(2) satisfies a Lipschite condition on any rectangle a<=x<b and c<=y<=d.

In the L-C Circuit   L= 1 HENRY , C 1/16 farad and E(t) =60 volt

The differential equation q’’ +16q’  = 60 represent the capacitor charger at anytime t

Q(0)=0 and q’(0) =0 = i(0) =0 find the charge q on the capacitor at anytime t

The indicated function y₁(x)

 is a solution of the associated homogeneous equation. Use the method of reduction of order to find a second solution y₂(x)

 of the homogeneous equation and a particular solution y_p(x)

 of the given nonhomogeneous equation.

y'' + y' = 1;    y₁ = 1

y₂(x)

= y_p(x)

=