Differential Equations Answers

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)

= 

Let an electrical circuit be governed by the following system of differential equation where i1,i2,i3 are the current in each branch of electrical circuit.find the current i1,i2,i3 internship branch of the electrical circuit by using diagonalisationmethod i1'=2i1+2i2+i3;i2'=i1+3i2+i3; i3'=i1+2i2+2i3

xydy/dx+4x²+y²=0 where y(2)=-7,x>0

Find the differential equation to the following;

dy/dx=9.8-0.196y

The continuous signal f(t) = cos(πt/2) sampled at 1 second intervals starting from t = 0.

(a) Find the Laplace transform of the sampled signal f*(t)

Solve the following IVP

y"-10y'+9y=5t;y(0)=-1,y'(0)=2