Purchase Solution

First order ODE Reduced to homogeneous ODE

Not what you're looking for?

Ask Custom Question

Given (t-3y-5) dt + (y-t+1) dy =0
introduce a change of variables to transform this ODE into a homogeneous one and solve.

Purchase this Solution
Solution Summary

Given (t-3y-5) dt + (y-t+1) dy =0
introduce a change of variables to transform this ODE into a homogeneous one and solve.

Solution Preview

Let t = ť -α
Let y = y'- β
where t' and y' are new variables, and α and β are constants to be determined.

Note: dt= dt' and dy = dy'

(t'- α + 3y' -3β -5) dt' + (y'-αβ - t'+αβ+1)dy' =0
(t'+3y' -α -3β-5) dt' +(-t'+y'+α -β +1) dy' = 0 (equation 2)

We want to find the values of α and β so that these ...

Purchase this Solution
Free BrainMass Quizzes
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.

Solving quadratic inequalities

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

Exponential Expressions

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

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Probability Quiz

Some questions on probability

View More Free Quizzes
Related BrainMass Solutions

  • solving differential equations

    Find both the first and second order differentials (y' and y") for the following functions: 2. Use integrating factor to convert the following equation into "exact ODE" form and solve for y. 2xy' = (y -x) (y + x)/ y 3.

  • Variation of Parameters

    We use variation of parameters to find the general solution to a given inhomogeneous second order linear ODE by first solving the homogeneous equation.

  • Solution to Second Order ODE

    Solution Homogeneous: Particular: Given Check answer: A Second Order ODE is solved. The solution is detailed and well presented.

  • Solve a homogenous 2nd order ODE.

    27338 Solve a homogenous 2nd order ODE : Cauchy-Euler Equation Find y as a function of x if: (x^2)(y'') + 19xy' +81y = x^2 y(1) = 9 y'(1) = -3 Hint: First assume that at least one solution to the corresponding homogeneous equation is of the

  • Ordinary differential equations

    dx => du/g(u) = dx/f(x) => variable separable this type of problem is called reducible to variable separable ( homogeneous eqn.: no constant ) Now next step can be non-homogeneous (heterogeneous) e.g.: dy/dx = (x +2y +1)/(2x+y+1) so first convert

  • Solving two independent ordinary differential equations. Concentrations of solute in flowing from one tank to another.

    Once this is done, we get sigma_(B,h)=C_1 e^(-vt/V) (10) In order to find the particular solution to the ODE given in (9), we must use our solution for the concentration in tank A (equation (8)).

  • Question about Second Order ODE

    solve for a, we have a= -1/21 Therefore y= is the special solution to (1) (2) Next we want to find solution to the homogeneous equation (y'')-7xy'-9y =0 (2) Let , then , ,then y'(x)= ,and (2) becomes y''(t)-y'(t)-7y'(t)-9y = 0 or

  • Sturm-Liouville: Eigenvalues, Eigenfunctions and Square Norm

    However, because the original ODE is homogeneous, any arbitrary normalization could be used.

  • Find the steady state solution for ODE

    86242 Find the steady state solution for ODE Find the steady state solution for non-homogeneous ODE as found in the attached file. Please see attached files. This problem can be solved using the elimination method.

View More Related Solutions