Reduction of Order? Help please.

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In summary, the conversation revolves around finding y2 if y1= x^(-1) and the equation x^2y"+3ty'+y=0. The solution provided is ln(x)/x using Abel's method, but there is uncertainty about its accuracy. The person is asking for confirmation and requesting to not lose any points on the online assignment.
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bigt9
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I think I have this right, its just its an online assignment and I don't want to lose any points on it.(1/4 my grade)

Question: Find y2 if y1= x^(-1) and the equation: x^2y"+3ty'+y=0.

I solved(using Abel's) for it:
ln(x)/x

but I am not entirely sure.

Wondering if I am spot on or am not doing it right/ thanks
 
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  • #2
bigt9 said:
I think I have this right, its just its an online assignment and I don't want to lose any points on it.(1/4 my grade)

Question: Find y2 if y1= x^(-1) and the equation: x^2y"+3ty'+y=0.

I solved(using Abel's) for it:
ln(x)/x

but I am not entirely sure.

Wondering if I am spot on or am not doing it right/ thanks

Welcome to the PF.

Can you please show the steps you used to arrive at that solution?
 

What is reduction of order?

Reduction of order is a mathematical technique used to solve a second-order linear differential equation by converting it into a first-order equation.

When is reduction of order used?

Reduction of order is typically used when one solution of a second-order differential equation is already known and the goal is to find a second independent solution.

What is the process of reduction of order?

The process of reduction of order involves substituting a new dependent variable for the known solution, reducing the differential equation to first-order, and then solving the resulting equation for the new dependent variable.

What are the benefits of using reduction of order?

Reduction of order allows for the solution of a second-order differential equation without having to use complex methods such as variation of parameters or undetermined coefficients.

Are there any limitations to using reduction of order?

Reduction of order can only be used to solve linear second-order differential equations with constant coefficients. It also requires the knowledge of one solution beforehand.

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