Purchase Solution

Solve the differential equation or initial value problem using the method for undetermined constants and variation of parameters.

Not what you're looking for?

Ask Custom Question

Solve the differential equation using the method of variation of parameters.
Solve the differential equation or initial-value problem using the method for undetermined constants.
y''-4y=e^x cosx y(0)=1, y'(0)=2

y''+y'- 2y=x - sin 2x y(0)=1, y'(0)=0

y'' + y = cot x 0<x<pi/2
See attached file for full problem description.

Attachments
Purchase this Solution
Solution Summary

ODEs and IVPs are solved. The solution is detailed and well presented.

Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

Solve the differential equation or initial-value problem using the method for undetermined constants
8.
(1) First the solution to the homogeneous differential equation
.
Its characteristic equation has 2 real roots, which are . So the solution is

(2) the particular equation to the differential equation
Assume it has the particular solution has the form of
Plug into the ...

Purchase this Solution
Free BrainMass Quizzes
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.

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.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

View More Free Quizzes
Related BrainMass Solutions

  • Differential equations

    Solve the differential equation...using variation of parameters method. Solve the initial value problem...

  • Differential Equations Variation of Parameters and Undetermined Coefficients and IVP

    Find a particular solution using the method of variation of parameters then find a general solution y" + 9y = cos(3x). 3. Solve the Initial Value Problem x" + 4x = 6sin(3t). x(0)=4, x'(0) = 0.

  • Variation of parameters and Undetermined coeeficients

    29062 Variation of parameters and Undetermined coefficients 1. Write a short paragraph comparing and contrasting the method of undetermined coefficients and variation of parameters. How are they similar, how they are different?

  • Initial value an derivation of parameters

    See the attached file. Please find the solution of differential equation problem in the attached file. The solution provides an example of solving an initial value problem using variation of parameters.

  • Step by Step Explanation of Differential Equations

    (I've never seen variation of parameters used for first order differential equations in any case - this method is usually used for second or higher orders.)

  • Method of Undermined coefficients

    In pages 4-6 I solve for the particular solution in the method of undetermined coefficients, including a MAPLE verification of the solution. In pages 7-10 I show how to use the method of variation of parameters.

  • Simple harmonic oscillation driven by an external force

    Now based on the Newton's second law, See the following problem of solving the above homogeneous differential equation. The general solution is Where So We then use the initial condition to find the constants c1 and c2.

  • Undetermined coefficients

    of working with undetermined coefficients to find a particular solution and use that solution to solve an initial value problem.

  • solving differential equations

    ODE is Therefore, the general solution to the given ODE is: Now find the constants c1 and c2 using the initial values: Differentiate y(x): Then Thus the solution of this IVP is: 5.

View More Related Solutions