Solve the differential equation - df/dt = 12t + (9t / square root of (4 -...

Solve the differential equation -

df/dt = 12t + (9t / square root of (4 - t^2)) + C

Expert Solution

milcah answered 2 years ago

t2 (d2r/dt2) - 9t (dr/dt) + 16r = 4 is an example of a "Cauchy-Euler equation."...

t2 (d2r/dt2) - 9t (dr/dt) + 16r = 4 is an example of a "Cauchy-Euler equation." Such equations appear in a number of physics and engineering applications. a) Write the complementary homogeneous equation. b) Plug r = ekt into the equation you wrote in part a. Show that this solution will not work for any constant k: this equation has no exponential solution. c) Plug the guess r = tn (where n is a constant) into the equation you wrote...

solve differential equation. y" + 9y = 18t^2 + 9t + 1 ; y(0) = 5/3...

solve differential equation. y" + 9y = 18t^2 + 9t + 1 ; y(0) = 5/3 ; y'(0) = 10

Solve the differential equation both by undetermined coefficients and the Laplace transform: d2y/dt2– 3 dy/dt +...

Solve the differential equation both by undetermined coefficients and the Laplace transform: d2y/dt2– 3 dy/dt + 2y = 6 exp(3t), y(0) = 6, y’(0) = 14.

Solve using the same approach as the solution using Matlab for this differential equation d^2y/dt^2 +...

Solve using the same approach as the solution using Matlab for this differential equation d^2y/dt^2 + 6dy/dt + 9y = cos(t) has initial conditions y(0)=1 y'(0)=2, Find Y(s) and without finding y(t), determine what function of time will appear in the solution %} clear, clc syms Y s t real rhs = laplace(cos(t),t,s) eqn1 = s^2*Y - s*2 - 1 + 6*s*Y -1 + 9*Y ==rhs myanss = solve(eqn1,Y) mypart = partfrac(myanss,'FactorMode','real') %{ mypart = (0.08*s + 0.06)/(s^2 + 1.0)...

find the solution to the differential equation. d^2y/dt^2 - 7dy/dt=0, y(0)=4, y'(0)=7

1) Use MATLAB to solve this differential equation. ??/?? = .25? (1 − ?/4 ) -...

1) Use MATLAB to solve this differential equation. ??/?? = .25? (1 − ?/4 ) - a 2) Use MATLAB to graph solution curves to this system with several different initial values. Be sure to show at least one solution curve for each of the scenarios found in ??/?? = .25? (1 − ?/4 ) - a ( let a = 0.16)

Question

Solve the differential equation - df/dt = 12t + (9t / square root of (4 -...

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t2 (d2r/dt2) - 9t (dr/dt) + 16r = 4 is an example of a "Cauchy-Euler equation."...

solve differential equation. y" + 9y = 18t^2 + 9t + 1 ; y(0) = 5/3...

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