# Ordinary differential equation

Solve the ode y'' - y' +4y = 0 as a system of first order odes.

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#### Solution Preview

set x_1 = y and x_2 = y' so that

x_1 ' = y' and

x_2 ' = y '' = y ' - 4y = x_2 - 4x_1

hence the given equation is equivalent to the system

X ' =

(0 1)

(-4 1) X

where X = [x_1 x_2] is a column vector.

The eigenvalues of the matrix ...

#### Solution Summary

This provides an example of solving an ordinary differential equation as a system of first-order ordinary differential equations.

Solutions to First-Order Ordinary Differential Equations

Question 1: (1 points)

Solve the following equations for given initial condition.

Please represent your answer in the implicit form ( ). Use y(x) instead of y

Question 2: (1 points)

Integrate the following equations and write a solution for given initial condition.

Please represent your answer in the implicit form ( ). Use y(x) instead of y.

Question 3: (1 points)

Integrate the following equations and write a nontrivial solution.

Please represent your answer in the implicit form ( ). Use MAPLE syntax. Use y(x) instead of y.

Question 4: (1 points)

Integrate the following equations and write a nontrivial solution.

Please represent your answer in the implicit form ( ). Use MAPLE syntax. Use y(x) instead of y.

Question 5: (1 points)

Integrate the following equations and write a nontrivial solution.

Please represent your answer in the implicit form ( ). Use MAPLE syntax. Use y(x) instead of y.

Question 6: (1 points)

Integrate the following equations and write a nontrivial solution.

Please represent your answer in the implicit form ( ). Use MAPLE syntax.

Question 7: (1 points)

Integrate the following equations and write a solution for given initial condition.

Please represent your answer in the explicit form ( ). Use MAPLE syntax. Use y(x) instead of y.

Question 8: (1 points)

Integrate the following equations and write a nontrivial solution.

Please represent your answer in the explicit form ( ). Use MAPLE syntax.

Question 9: (1 points)

Solve the following equation

Please represent your answer in the implicit form ( ), Use MAPLE syntax. Use y(x) instead of y.

Question 10: (1 points)

Make the change of variable for the homogenous differential equation

and find , where

Question 11: (1 points)

Solve the following equation

Please represent your answer in the explicit form ( ), Use MAPLE syntax. Use y(x) instead of y.

Question 12: (1 points)

Find the general solution of the linear differential equation (use C to denote a constant)

.

Question 13: (1 points)

Find the solution of the linear differential equation which satisfies the initial condition :

.

Question 14: (1 points)

Find the solution of the following differential equation:

.

Question 15: (1 points)

Solve the following equation for given initial condition

Please represent your answer in the explicit form ( ), Use MAPLE syntax. Use y(x) instead of y.

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