find the solution y(t) to each of the following equations given the initial condition 3= (0)...
Find a particular solution satisfying the initial condition, of each of the following differential equations 17-21. The initial condition is indicated alongside each equation. 3xy? dz, y(2) y dy + x d = = 1.
(15 pts) Given the following differential equations with the initial condition y(0) = 1, determine (1) the zero-input response yzi(t), (2) the zero-state response yzs (t) and (3) the total response y(t) for the input x(t) = e-fu(t) by using Laplace Transform. (5 pts) x+6y(t) = x - x() (1) Yzi(t) = (2) yzs(t) = (3) y(t) = (5 pts) (5 pts) 2. (10 pts) Given the following differential equations, find the total response y(t) if y(0) = 1 for...
Problem 3. Find the general solution of the following first order differential equations. If an initial condition is given find the specific solution. a) xy'y - exy. Suggestion: Set u xy c) y, + 2xy2-0 , y(2)-1
Find the solution to the given system that satisfies the given
initial condition.
Find the solution to the given system that satisfies the given initial condition. -7 -1 x(t) = x(t), 2-5 - 5 2 (a) (0) = (b) x(t) = (c) x( - 2) = 21 (d) (2) = 0 1 1
Find the solution of a = y (6 - ) satisfying the initial condition y(0) = 90. (Use symbolic notation and fractions where needed.) y = Find the solution of = y(6 - ) satisfying the initial condition y(0) = 18. (Use symbolic notation and fractions where needed.) y = Find the solution of a = y(6 - ) satisfying the initial condition y(0) = -6. (Use symbolic notation and fractions where needed.) y =
Find the solution of the given initial value problem: y" + y = f(t); y(0) = 6, y'(0) = 3 where f(t) = 1, 0<t<3 0, įst<<
Find the solution of a = y (5 – š) satisfying the initial condition y(0) = 100. (Use symbolic notation and fractions where needed.) y = Find the solution of = y (5 – }) satisfying the initial condition y(0) = 25. (Use symbolic notation and fractions where needed.) y = Find the solution of a = y (5 – š) satisfying the initial condition y(0) = -5. (Use symbolic notation and fractions where needed.) y =
Solve the given differential equation with initial condition. y'-6y = 0, y(0) = 9 The solution is y(t) = (Type an exact answer.)
Find the solution to the given system that satisfies the given initial condition. _9_0 -9 x'(t) = 1 2 0 (x(t), 9_0 -5 ܕ (a) x(0)=1 (b) x( -r'- ܝ ܬ . 1 - 4 (a) x(f)- (Use parentheses to clearly denote the argument of each function.)
differential equations
y(0)=3
Read each problem carefully. Show all your work. Turn off your phones. No calculators! X1. Consider the differential equation y' = -y(y + 1)(y-4). (a) (3 points) Find the equilibrium solution(s) (y = 0). (b) (3 points) Sketch the direction field. (4 points) Sketch the solution y(t) with initial condition y(0) = -1. Sketch another solution y(t) with initial condition y(a) = 3.