4. (6 points) Determine the particular solution to the differential equation dy = x + 2y,...
Find the particular solution such that y=0 when t=0 of the differential equation: (dy/dt) - 2y = t
Dif equations 4
4. a) Determine whether the following differential equation is exact. (x + 2y) dx + (2x - y)dy = 0 b) Find the general solution using the method of exact differentials.
Find a particular solution to the differential equation using the Method of Undetermined Coefficients. dy dy -5 + 2y = x e* dx? dx A solution is Yp(x) =
Find the particular solution of the following first order linear
differential equation
dy dr - Y= CON 2 Fe2r,y(0) = -1
4. Consider the differential equation +2y + 2y = cost (a) (5 points) Find the general solution to the corresponding homogeneous equa- tion. (b) (5 points) Find a particular solution, y(t), to the non-homogeneous equation. (c) (2 points) Determine the general solution to the non-homogeneous equation.
1. (4 points) Determine whether the given function y, given explicit or implicit, is a solution to the corresponding differential equation a) y = 2* +3e2a; y" - 3y + 2y = 0. dy 2.ry b) y - In y = r2+1, (Use implicit differentiation) dr y-1 2. (3 points) Find the solution to the initial value problem: dy = e(t+1); y(2) = 0 dr 3. (3 points) Find the general solution to the following equation. y dy ada COS
4. Consider the homogeneous differential equation dy d y dy-y=0 dx3 + dx2 dx - y (a) Show that 01 (C) = e is a solution. (b) Show that 02 (2) = e-* is a solution. (c) Show that 03 (x) = xe-" is a solution. (d) Determine the general solution to this homogeneous differential equation. (e) Show that p (2) = xe" is a particular solution to the differential equation dy dy dy dx3 d.x2 - y = 4e*...
Find a particular solution to the differential equation using the Method of Undetermined Coefficients. dPy dy -7 + 2y=x e* dx ox? A solution is yp(x)=
(10 points) For the differential equation y(6) - 2y (5) – 3y(4) + 2y(3) + 10y" – 8y = 0. Find the fundamental solution set to the DE if the characteristic equation in factored form is given by (r – 2) (r2 + 2r + 2) (r - 1) (r + 1) = 0
4) (25 points) Find the particular solution of the differential equation. Use dy 4x4 separation of variables. dx y4 y(0)=2 5) (15 points) For a certain drug, the amount y(t) remaining in the blood after t hours satisfies y' = -0.1y with y(0=2 mg. Find y(t) and use your answer to estimate the amount present in the blood after 2 hours. (Hint: use the appropriate unlimited, limited or logistic model from the Models of Growth table. State the model you...