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