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y'=(2cos^2(x)-sin^2(x)+y^2)/2cos(x), y(0)=-1, y(1)=sin(x)
In an L-C circuit, L = 1 henry, C = 1
16 farad and E(t) = 60 volt.
Solce using laplace
dt dt represents the capacitor charge at anytime t.
Given q(0)= 0and q' ( 0)=i(0)=0 find:
7.1 the charge q on the capacitor at anytime t. (7)
7.2 the current i at anytime t.
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
