Find the general solution to the differential equation

Find the general solution to the differential equation
y'+(12x^11)y=x^12

Use the variable I= the integral of e^(x^12)dx where it occurs in your answer.

According to some people, it doesn't have an elementary solution, look at:
http://www.wolframalpha.com/input/?i=y%27+%2B+12*x^11*y+%3D+x^12

there's a incomplete gamma function ?

can someone please show me how to solve this problem, thank you so much!

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Hi ani9890! Welcome to PF

Wolfram Alpha has a strange way of solving differential equations. But there is an elementary solution, as it is a simple linear differential equation. How can you solve such equations?

Hint : Start by analyzing what the integrating factor is...

so I end up with this,

d/dx[ye^(x^12)] = x^12*e^(x^12)

and I'm supposed to integrate both sides, but the right side can't be integrated to give a elementary solution. So what should I do?

I was thinking y(x)=e^(-x^12)(x^12)I
where I stands for the integral of e^(x^12) , but I'm sure this is wrong lol

SammyS
Staff Emeritus
Homework Helper
Gold Member
so I end up with this,

d/dx[ye^(x^12)] = x^12*e^(x^12)

and I'm supposed to integrate both sides, but the right side can't be integrated to give a elementary solution. So what should I do?

I was thinking y(x)=e^(-x^12)(x^12)I
where I stands for the integral of e^(x^12) , but I'm sure this is wrong lol
No:

$\displaystyle \frac{d}{dx}\left(ye^{\displaystyle x^{12}}\right)=y'\ e^{\displaystyle x^{12}}+y\,e^{\displaystyle x^{12}}\left(12x^{11}\right)$

So, what if you multiply your Dif.Eq. by e12x ?