Explore BrainMass
Share

Explore BrainMass

    Solutions to First-Order Ordinary Differential Equations

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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.

    © BrainMass Inc. brainmass.com April 3, 2020, 10:31 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/solutions-first-order-ordinary-differential-equations-446611

    Attachments

    Solution Preview

    Please see the attachment.

    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

    This is a separable differential equation. We write it as
    .

    Integrating both sides we obtain

    for some constant c. Plugging in the initial condition we obtain

    whence . Thus the solution is , or

    The implicit form of this equation is .

    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.

    Dividing both sides by we obtain

    which is separable, so we write it as

    .
    Integrating both sides we obtain

    .

    Exponentiating both sides we now obtain

    .

    Plugging in the initial condition we obtain

    .

    Thus the solution is , or .

    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.

    This is another separable differential equation. Separating variable and integrating both sides we obtain
    .
    To evaluate the integral on the right (with the minus sign), we make the substitution , whence and the integral becomes

    .

    Similarly, the integral on the left becomes

    .

    Thus we have

    whence

    ,

    which yields a nontrivial solution for any constant c such that . For instance, when we have the nontrivial solution .

    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.

    This is another separable ...

    Solution Summary

    We solve several first-order ordinary differential equations. Implicit equations are examined.

    $2.19

    ADVERTISEMENT