The differential equation R+=0 describes the charges P coulombs at time t (in seconds), where C and R are the capacitance (in farads) and resistance (in ohms). respectively. (a) Solve the equation for P. given P = P₁ at t = 0. (b) Given the capacitance and resistance of a circuit to be 6.5 x 10 °F and 225 x 10³0. respectively. After 0.29 seconds the charge falls to 7 coulombs. Calculate the initial charge. Then, determine the charge after 1.5 seconds.
The differential equation R+=0 describes the charges P coulombs at time t (in seconds), where C and R are the capacitance (in farads) and resistance (in ohms). respectively. (a) Solve the equation for P. given P = P₁ at t = 0. (b) Given the capacitance and resistance of a circuit to be 6.5 x 10 °F and 225 x 10³0. respectively. After 0.29 seconds the charge falls to 7 coulombs. Calculate the initial charge. Then, determine the charge after 1.5 seconds.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Question 1
The differential equation R+=0 describes the charges P coulombs at time t (in
seconds), where C and R are the capacitance (in farads) and resistance (in ohms),
respectively.
(a) Solve the equation for P. given P = Po at t = 0.
(b)
Question 2
Find the general solution of the equation (x²-x-2)=x-3y(x-1) + 1.
(a)
Given the capacitance and resistance of a circuit to be 6.5 x 10-F and 225 x 10³0.
respectively. After 0.29 seconds the charge falls to 7 coulombs. Calculate the initial
charge. Then, determine the charge after 1.5 seconds.
(b) The boundary conditions for the ODE in (a) is given as y = 5 at x = -1, find the
particular solution of the equation in (a).
Question 3
Given the following non-homogeneous second-order ordinary differential equation,
y" - 2ky' + k²y = 12xekx, k>0
(a) Find a general solution of the ODE, provided that y = Px³ekx is part of the solution,
where P is a constant.
(b)
Let y = 1, y'= 0 at x = 0, show that
yekx (2x³-kx + 1)
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