(a) Use separation of variables to find the solution of the following differential equation with initial condition dy / dt= y^2(e^2t + 1), y(0) = 1.
(a) Use separation of variables to find the solution of the following differential equation with initial condition
dy / dt= y^2(e^2t + 1), y(0) = 1.
(b) Consider the following second order differential equation:
y^n(t) + 4y'(t)+ 3y(t) = 3t + 2.
(i) Find the general solution of the homogeneous version of the problem.
(ii) A particular solution of the nonhomogeneous equation has the form yP = A1t + A0. Find the values of A1 and A0
(c) Consider the following differential equation:
y^n(t) + 4y'(t) + αy(t) = 0,
where α is a constant.
Determine the value, or range of values, of α for which the solution to the equation is of the form
(i) y = c1e^at cos(bt) + c2e^at sin(bt),
(ii) y = c1e^at + c2te^at
.
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(c) Consider the following differential equation:
y^n(t) + 4y'(t) + αy(t) = 0,
where α is a constant.
Determine the value, or range of values, of α for which the solution to the equation is of the form
(i) y = c1e^at cos(bt) + c2e^at sin(bt),
(ii) y = c1e^at + c2te^at
by Bartleby Expert(b) Consider the following second order differential equation:
y''(t) + 4y'(t)+ 3y(t) = 3t + 2.
(i) Find the general solution of the homogeneous version of the problem.
(ii) A particular solution of the nonhomogeneous equation has the form yP = A1t + A0. Find the values of A1 and A0
(c) Consider the following differential equation:
y^n(t) + 4y'(t) + αy(t) = 0,
where α is a constant.
Determine the value, or range of values, of α for which the solution to the equation is of the form
(i) y = c1e^at cos(bt) + c2e^at sin(bt),
(ii) y = c1e^at + c2te^at
by Bartleby Expert
