A second ODE problem that bothers me a lot HELP

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In summary, the conversation discusses two ODE problems and finding the solutions for each with different initial conditions. The characteristic equation is used to solve the problems and the person had some trouble initially but eventually found the correct solutions.
  • #1
A second ODE problem that bothers me a lot~~ HELP!

The question is like:
Find the function y1 of t which is the solution of:
with initial conditions y1(0)=1, y'1(0)=0

y1= ?

Find the function y2 of t which is the solution of:
with initial conditions y2(0)=0, y'2(0)=1

y2= ?

Find the Wronskian W(t)= W(y1.y2)


The way I tried to achieve the problem is to solve the characteristic equation, which is
9r2-36r-45=0, which gives r1=5 and r2=-1; then I consider y1 and y2 are exp(r1) and exp(r2) respectively. But it seems my answer is wrong...
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  • #2

never mind, I got it.

1. What is an ODE problem?

An ODE (ordinary differential equation) problem is a mathematical problem that involves finding a function that satisfies a given differential equation. It is commonly used to model various physical systems and phenomena.

2. What is a second ODE problem?

A second ODE problem is a specific type of ODE problem where the differential equation involves a second derivative of the unknown function. This means that the equation involves the function itself, its first derivative, and its second derivative.

3. Why does the second ODE problem bother you?

The second ODE problem can be challenging to solve because it requires knowledge of advanced mathematical concepts such as calculus and differential equations. It can also have multiple solutions or no solution at all, making it a difficult and frustrating problem for many scientists.

4. Can you provide an example of a second ODE problem?

One example of a second ODE problem is the harmonic oscillator, which models the motion of a mass attached to a spring. The equation is given by mx'' + kx = 0, where m is the mass, k is the spring constant, and x is the position of the mass.

5. How can I approach solving a second ODE problem?

There are various methods for solving second ODE problems, such as separation of variables, substitution, and power series. It is important to have a solid understanding of calculus and differential equations, as well as practice and patience when approaching these types of problems.

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