First order differencial equation

[Tsotne]

Can you solve: dy/dt + ln(t) * y = -sin(t) * y''

In numerical methods not analitically

 

[mLwin]

Domain? Tolerance? Neighborhood for solution? And with the y" term, it's not a first-order diff equation.

 

[pruse]

discretize, of course!

 

[Tsotne]

it's not a first-order diff equation.

Yes correct I modified it after stating the first order diff. equation.

dy/dt + ln(t) * y = -sin(t) This is it. Analytically.

 

[pruse]

Analytically.

numerically... analytically... well which is it?

 

[Jonathan]

RK4 for 1st order ODEs

 

[Tsotne]

numerically... analytically... well which is it?

Analytically. The trouble is that on the right side there appears sin(t) * (t^t) * exp(t)

 

[mLwin]

If you want an analytic solution, closed form solutions for first-order diff eqs are well-known and, for the most part, tractable. Use an integrating factor.

(y(t) = e^{-t\ln t + t}\bigg( C + \int \sin(t) e^{t\ln (t) - t} dt \bigg))

 

[Daniel Duffy]

If you want an analytic solution, closed form solutions for first-order diff eqs are well-known and, for the most part, tractable. Use an integrating factor.

(y(t) = e^{-t\ln t + t}\bigg( C + \int \sin(t) e^{t\ln (t) - t} dt \bigg))

http://en.wikipedia.org/wiki/Integrating_factor

 

[koupparis]

I think the OP was looking for an closed form solution to the sin(t)e^(stuff) integral. I don't think you're going to find a closed form solution to this.

 

[Amber Roxanna]

huh ? what is this ?