Difficulty checking the solution of differential equation

asadpasat
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Homework Statement


The differential equation is xy'-2y= x3ex
Check the solution y=x2 ex

Homework Equations


Just plug in

The Attempt at a Solution


y' = x2ex + 2xex
Having problem solving for x.
 
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Why are you trying to solve for x? Just substitute your solution for y into the differential equation.

Chet
 
asadpasat said:

Homework Statement


The differential equation is xy'-2y= x3ex
Check the solution y=x2 ex

Homework Equations


Just plug in

The Attempt at a Solution


y' = x2ex + 2xex
Having problem solving for x.
Why solve for x ?

Like you said, "Just plug in".
 
omg, got it. thanks a lot
Chestermiller said:
Why are you trying to solve for x? Just substitute your solution for y into the differential equation.

Chet
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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