Solve the System of Differential Equations

Subject to the conditions x(0) = 0 and y(0) - 1, completely solve the following system of differential equations: x' = x y' = xy + e^t

System of Differential Equations : Find Equilibrium Points and Linearize

Consider the attached system of differential equations. x' = xy + x y' = xy + y^2 a. Find the equilibrium points associated with this system. b. Linearize the system about each of the equlibrium points you find in part a.

Solve the Differential Equation subject to initial conditions.

Solve, subject to the given initial conditions: x(0) = x'(0) = 0 solve x'' + x = sec t t ε (-pi/2, pi/2)

Systems of Differential Equations : General Solution and Phase Portrait

a. Find the general solution to the attached system of differential equations. x' = y y' = 2x b. Draw the phase portrait for this system and describe in words what happens to the solution for all initial conditions: x(0) = x0 and y(0) = y0

ODE : Phase Portrait and Rough Sketch of a Solution at Specific Points

Draw the phase portrait associated with x'' - 2x' + 2x = 0 and draw a rough sketch of the solution x(t) that satisfies x(0) = 1 and x'(0) = 0.

Ode (Eigenvalues; Eigenvectors)

Let A = {see attachment} a. Solve x' = Ax b. Solve x' = Ax subject to x(0) = 0

using malthus method

suppose that a culture of bacteria has initial population of n=100. If the population doubles every three days, determine the number of bacteria present after 30 days. How much time is required for the population to reach 4250 in number

Solve the Differential Equation.

Please give me a step-by-step solution to this attached ODE. x'' + x = d2(t) + u2(t) x(0) = 0 x'(0) = 0 Please see the attached file for the fully formatted problems.

Third Order Taylor Polynomial Approximation of Solution to an ODE

Find a third order Taylor polynomial approximation, centered at t=0, of the solution to: x''+tx =0 x(0)=1 x'(0)=1

Simple ODE

Please give me a step-by-step solution to this attached ODE. Thanks