What am I doing wrong? - Linear Differential Equations

In summary, the problem involves solving a linear differential equation with the initial condition y(1)=1. The solution method involves using P(x) and Q(x) and plugging in values for x and y to solve for the constant c. The attempt at solving the equation resulted in conflicting values for c, but it was determined that c=6/7 is the correct answer. However, when plugging this value into the equation, the program is still indicating an incorrect answer.
  • #1
lelandsthename
12
0
What am I doing wrong?? - Linear Differential Equations

Homework Statement


Hi everyone, the problem I have is listed under my attempt (I hope it's ok that I pasted it): to solve the below linear differential equation with the initial condition y(1)=1

Homework Equations


P(x) and Q(x) linear differential equation solution method

The Attempt at a Solution


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Plugging in for 1=y and 1=x to solve for c has yielded me crazy results after i plugged in y^(-2). I got both c=6/7 and c=-1/6 but neither are the correct answer (this problem is listed on a program that allows me to check my answer) can anyone help me explain if I did a step wrong or if I am solving for C wrong??

Thanks!
 
Last edited:
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  • #2


I don't know why you say "crazy results". If y= 1, then z= 1 also so your last equation becomes 1= 1/7 + C and C= 6/7 is the only result.

y-2= -(1/7)x-4+ (6/7)x-18 gives

[tex]y^2= \frac{1}{-(1/7)x^{-4}+ (6/7)x^{-18}}= \frac{-7}{x^{14}- 6}[/tex]
 
  • #3


Well the crazy results come when i plug my answer into y=. The program keeps telling me that I am incorrect with
[tex]\sqrt{7x^4}+((7x^{18})/6)[/tex]
(that's to the 18th)
 

1. What are linear differential equations?

Linear differential equations are mathematical equations that involve a function and its derivatives. The function and its derivatives are represented as a linear combination, where the coefficients are constants. These equations are widely used in physics, engineering, and other fields to model various phenomena.

2. What is the most common mistake when solving linear differential equations?

The most common mistake when solving linear differential equations is forgetting to account for the constant of integration. This constant is necessary because when finding the antiderivative of a function, there is an infinite number of possible solutions. Therefore, the constant of integration is added to account for all possible solutions.

3. How do I know if I am using the correct method to solve a linear differential equation?

There are several methods for solving linear differential equations, such as separation of variables, integrating factors, and variation of parameters. The best method to use depends on the form of the equation and the initial conditions given. It is important to carefully analyze the equation and choose the most appropriate method.

4. Can linear differential equations be solved analytically or numerically?

Linear differential equations can be solved both analytically and numerically. Analytical solutions involve finding an exact formula for the solution, while numerical solutions involve using numerical methods to approximate the solution. In some cases, it may not be possible to find an analytical solution, and a numerical approach is necessary.

5. How can I check if my solution to a linear differential equation is correct?

To check if your solution to a linear differential equation is correct, you can plug the solution back into the original equation and see if it satisfies the equation. You can also check if the initial conditions are satisfied by the solution. Additionally, you can use a graphing calculator or software to graph both the original equation and your solution and see if they match up.

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