let's firstly convert the mixed fraction to improper fraction and then take it from there, keeping in mind that the whole is "x".
X+5÷9=3 What is the number where when you add 5 then divide it by 9 it is 3?
2 answers:
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Rearrange the ODE as
Take
, so that 
.
Supposing that
, we have 
, from which it follows that
So we can write the ODE as
which is linear in
. Multiplying both sides by 
, we have
![\dfrac{\mathrm d}{\mathrm dx}\bigg[e^{x^2}u\bigg]=x^3e^{x^2}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5Be%5E%7Bx%5E2%7Du%5Cbigg%5D%3Dx%5E3e%5E%7Bx%5E2%7D)
Integrate both sides with respect to
:
![\displaystyle\int\frac{\mathrm d}{\mathrm dx}\bigg[e^{x^2}u\bigg]\,\mathrm dx=\int x^3e^{x^2}\,\mathrm dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint%5Cfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5Be%5E%7Bx%5E2%7Du%5Cbigg%5D%5C%2C%5Cmathrm%20dx%3D%5Cint%20x%5E3e%5E%7Bx%5E2%7D%5C%2C%5Cmathrm%20dx)
Substitute
, so that 
. Then
Integrate the right hand side by parts using
You should end up with
and provided that we restrict, we can write
Take
Supposing that
So we can write the ODE as
which is linear in
Integrate both sides with respect to
Substitute
Integrate the right hand side by parts using
You should end up with
and provided that we restrict
