Is the question solve y'' = x^3/y a misprint?

[Damned charming :)]

I saw a first year question solve y''=x^3/y
I am assuming that this is a misprint because
solving y'= x^3/y is easy because it is separable
but I have no idea how to solve
y'' = x^3/y

 

[Damned charming :)]

I feel quite silly for not noticing the differential equations forum, How do I get this thread moved.

 

[Fredrik]

I feel quite silly for not noticing the differential equations forum, How do I get this thread moved.

Use the "report" button and ask that it be moved.

 

[HallsofIvy]

I feel quite silly for not noticing the differential equations forum, How do I get this thread moved.

Done!

 

[jackmell]

I saw a first year question solve y''=x^3/y
I am assuming that this is a misprint because
solving y'= x^3/y is easy because it is separable
but I have no idea how to solve
y'' = x^3/y

Try going to Wolfram Alpha and typing:

DSolve[y''[x]==x^3/y[x],y,x]

That give you a quick and simple way to test if it's simple but keep in mind there are rare exceptions. So if Alpha can't solve it, then there is a good chance it's either not easy to solve and so would not be a first-year question or it was meant to be solved numerically which I think could be first-year.

Also if you're interested, just type DSolve[y''[x]+y[x]==0,y,x] just so you know what it looks like when it can solve it.

For the record I do not advocate students turning to Alpha to do their homework. Please try and learn how to do it yourself then learn how to use a CAS to reinforce your understanding of the subject. :)

 

[Damned charming :)]

Mathematica cannot seem to do it,

It can solve y'' = 1/y

The solution is
e to the power of a complicated function of the Inverse of the intergral of e^-(x^2)

I cannot see how multiplying by x^3 would make it easier.

I would bet a reasonable sum of money on it being a misprint.

 

[jackmell]

. . . suppose it's not a mis-print. This is a DE forum after all. Then what? Know about that BP oil-spill in the Gulf? That's not an easy one either. That's how it is in real life. Nothing like (a majority of) the textbook equations. Suppose you had to solve it. What do you do?

This is what I'd try:

$\sum_{n=0}^{\infty}a^n x^n \sum_{n=2}^{\infty} n(n-1)a_n x^{n-2}=x^3$

$\sum_{n=0}^{\infty}\sum_{k=0}^{n} a_{2+k}(2+k)(1+k)a_{n-k}x^n=x^3$

with $a_0$ and $a_1$ arbitrary and $a_0\ne 0$ since it's singular at $y(x)=0$

 

[ross_tang]

I have found a particular solution:

$$y(x)=\frac{2}{\sqrt{15}}x^{\frac{5}{2}}$$

Please refer to this:

http://www.voofie.com/content/75/how-to-solve-non-linear-second-order-differential-equation-given-a-particular-solution/"

It talks about how to solve for the particular solution. However, I am getting stuck in finding the general solution. Hope someone can help too.