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Impossible for me to integrate?? watch

1. Me again... I'm doing an FP2 diff eq question, and I've come to a standstill.
Here's the question:

dx/dt + 6x/t = 2sqrt(x) e^(-t^2)
Using the substitution z = x^(1/2) , solve the above differential equation.

What I have:

2z dz/dt + 6z^2/t = 2z e^(-t^2)

dx/dt + 3z/t = e^(-t^2)

t^3 dz/dt + 3z t^2 = t^3 e^(-t^2)

d(z t^3)/dt = t^3 e^(-t^2)

z t^3 = S t^3 e^(-t^2) dt

Now, how on earth do I integrate ???????? We haven't covered that at all!

edit: **** latex
2. (Original post by StarvingAutist)
Me again... I'm doing an FP2 diff eq question, and I've come to a standstill.
Here's the question:

What I have:

Now, how on earth do I integrate ???????? We haven't covered that at all!
Firstly, e^(-t^2) has no elementary antiderivative ie you can't integrate it. You can however integrate .

Spoiler:
Show

Consider the substitution
3. (Original post by StarvingAutist)
Me again... I'm doing an FP2 diff eq question, and I've come to a standstill.
Here's the question:

dx/dt + 6x/t = 2sqrt(x) e^(-t^2)
Using the substitution z = x^(1/2) , solve the above differential equation.

What I have:

2z dz/dt + 6z^2/t = 2z e^(-t^2)

dx/dt + 3z/t = e^(-t^2)

t^3 dz/dt + 3z t^2 = t^3 e^(-t^2)

d(z t^3)/dt = t^3 e^(-t^2)

z t^3 = S t^3 e^(-t^2) dt

Now, how on earth do I integrate ???????? We haven't covered that at all!

edit: **** latex
You actually want , which is considerably simpler. Substitute .
4. (Original post by ThatPerson)
Firstly, e^(-t^2) has no elementary antiderivative ie you can't integrate it. You can however integrate .

Spoiler:
Show

Consider the substitution
(Original post by Smaug123)
You actually want , which is considerably simpler. Substitute .
Thanks. I'm such a retard.
5. (Original post by StarvingAutist)
Thanks. I'm such a retard.
No problem - happens to us all!
6. IIRC, e^x^2 is a Gaussian Integral and it doesn't have an indefinite integral.
That said, I never did Further Maths and I've only briefly covered Gaussian Integrals as part of my first term of a Chemistry degree.

http://en.wikipedia.org/wiki/Gaussian_integral
7. (Original post by Smaug123)
No problem - happens to us all!
Some more than others
8. (Original post by TheWiseSalmon)
IIRC, e^x^2 is a Gaussian Integral and it doesn't have an indefinite integral.
That said, I never did Further Maths and I've only briefly covered Gaussian Integrals as part of my first term of a Chemistry degree.

http://en.wikipedia.org/wiki/Gaussian_integral
Yeah, the error function is what came up on wolfram alpha.

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