Purchase Solution

# Solve a homogenous 2nd order ODE.

Not what you're looking for?

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 form . You may have to use some other method to find the second solution to make a fundamental set of solutions. Then use one of the two methods to find a particular solution.

##### Solution Summary

A homogenous 2nd order ODE is solved. The expert solves a homogenous 2nd order ODE. A Cauchy-Euler equation is examined.

##### Solution Preview

This is a Cauchy-Euler equation. To solve that we let x=exp(z) and plug this into the equation. In general with this change of variable the equation:
x^2y''+ axy'+ by= f(x) becomes:

y''+ (a-1)y'+ by= f(exp(z)) ...

##### Probability Quiz

Some questions on probability

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

##### Graphs and Functions

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

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Exponential Expressions

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