Purchase Solution

Solutions to First-Order Ordinary Differential Equations

Not what you're looking for?

Ask Custom Question

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.

Attachments
Purchase this Solution
Solution Summary

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

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 ...

Purchase this Solution
Free BrainMass Quizzes
Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

View More Free Quizzes
Related BrainMass Solutions

  • ordinary differential equations

    Equations If an ODE only contains first derivatives, we call it a first order differential equation.

  • Series Solutions of Second Order Linear Equations : Ordinary Point, General Solution, Power Series and Radius of Convergence

    54048 Series Solutions of Second Order Linear Equations Verify that x0=0 is an ordinary point of the differential equation: y''+ xy' + 2y = 0 Find two linearly independent solutions to the differential equation in the form of a power series about x0

  • Step by Step Explanation of Differential Equations

    Taking the partial derivative of (***) with respect to y yields: (please see the attached file). The solution solves several first order ordinary differential equations using various methods.

  • Lipschitz Continuity and Initial Value Problems for ODE's

    Lipschitz continuity and its role in the existence and uniqueness of solutions to ordinary differential equations is investigated. Three problems are solved. The first is to show that a given function is Lipschitz continuous.

  • Non Linear System - Second Order System

    we get, dx2/dt = (1/M)*[ -kx1 -Fb*x2 ] Thus, we get the pair of first-order differential equations: dx1/dt = x2 and dx2/dt = (1/M)*[ -kx1 -Fb*x2 ] Note that these are now expressed as two, first order ODE's (Ordinary Differential Equations

  • Differential equations

    This provides examples of working with differential equations, including classifying, writing differential equations to fit descriptions, determine whether functions and relations are solutions, and determining whether an initial value problem has a solution

  • Ordinary Differential Equations

    Step-by-step solutions to the ordinary differential equations are provided.

  • Second Order Linear Differential Equations

    168615 Second Order Ordinary Linear Differential Equations with Constant Coefficients 1). Given the differential equation for 1. L[y]= y''+2by'+b2y = exp(-bx)/x2, x>0 ; a) Find the complementary solution of (1) by solving L[y] = 0.

  • Ordinary first order differential equation

    26896 Ordinary first order differential equation Find all solutions to the ODE yy'= (1-y^2) sin x. (When dividing by 1-y^2, be careful that you don't lose any solutions).

  • First order ordinary differential equation

    23866 First order ordinary differential equation In order to solve differential equations, it is helpful to classify them as belonging to one or more categories.

View More Related Solutions