Homogeneous Linear Systems

Practice Questions

Differential Equations › Homogeneous Linear Systems

Questions

10

1

Solve the homogenous equation:

With the initial conditions:

2

Find the general solution to the given system.

$\\frac{dx}{dt}=x+2y \\\frac{dy}{dt}=2x+y$

3

Solve the differential equation:

Subject to the initial conditions:

4

Solve the differential equation for y:

Subject to the initial condition:

5

Solve the second order differential equation:

Subject to the initial values:

6

Solve the initial value problem $\mathbf{x'} = \begin{bmatrix} 3&-2 \ -1&2 \end{bmatrix}\mathbf{x}$ . Where $\mathbf{x}_0 = \begin{bmatrix} 1\-1 \end{bmatrix}$

7

Solve the third order differential equation:

8

Find the general solution to the system of ordinary differential equations

$\widehat{x}^{'}(t) = A \widehat{x}(t)$

where

$A = \begin{bmatrix} 1 & 3\ 12 & 1 \end{bmatrix}$

9

When substituted into the homogeneous linear system $\mathbf{x'} = A\mathbf{x}$ for , which of the following matrices will have a saddle point equilibrium in its phase plane?

10

Find the general solution to the given system.

$\\frac{dx}{dt}=x+2y \\\frac{dy}{dt}=2x+y$

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