Solving Implicit O.D.E: sin(y) + xy - x^3 = 2 | 2nd Order ODE Help

  • Thread starter Thread starter AST3019
  • Start date Start date
AST3019
Messages
4
Reaction score
0
Is, sin(y) + xy - x^3=2, an implicit soln to the 2nd order ODE y''= {6xy' + (y')^3 * sin(y) - 2(y')^2}/ (3x^2 - y)?
 
Physics news on Phys.org
Have you tried it? If sin(y) + xy - x^3=2 then cos(y)y'+ y+ xy'- 3x^2= 0. Differentiating again, -sin(y)(y')^2+ cos(y)y''+ 2y'+ xy''- 6x= 0.

You can you those to see if the differential equation is satisfied or not.
 
thanks.
 

Thread 'Volterra equation of the second kind'

There is the following linear Volterra equation of the second kind $$ y(x)+\int_{0}^{x} K(x-s) y(s)\,{\rm d}s = 1 $$ with kernel $$ K(x-s) = 1 - 4 \sum_{n=1}^{\infty} \dfrac{1}{\lambda_n^2} e^{-\beta \lambda_n^2 (x-s)} $$ where $y(0)=1$, $\beta>0$ and $\lambda_n$ is the $n$-th positive root of the equation $J_0(x)=0$ (here $n$ is a natural number that numbers these positive roots in the order of increasing their values), $J_0(x)$ is the Bessel function of the first kind of zero order. I...
View full post »

Thread 'Visual Representation of Separation of Varables'

Are there any good visualization tutorials, written or video, that show graphically how separation of variables works? I particularly have the time-independent Schrodinger Equation in mind. There are hundreds of demonstrations out there which essentially distill to copies of one another. However I am trying to visualize in my mind how this process looks graphically - for example plotting t on one axis and x on the other for f(x,t). I have seen other good visual representations of...
View full post »

Similar threads

I Solving Differential Equation Using Reduction of Order
Replies
2
Views
3K
MHB B.2.1.4 trig w/ integrating factor
Replies
1
Views
1K
I Converting Second Order ODE to Hypergeometric Function
Replies
7
Views
3K
I Question about solving linear first order non-homogeneous ODEs
Replies
3
Views
3K
I Solve second order linear differential equation
Replies
7
Views
2K
MHB 2.2.8 de xy'+2y=sin x,y(pi)=1/pi find solution
Replies
2
Views
2K
I Trying to obtain a 2nd order ODE
Replies
6
Views
2K
MHB How Do I Solve this 2nd Order Non-Linear ODE and Find Its Equilibrium Points?
Replies
3
Views
3K
Find the local maxima and minima for##f(x,y) = x^3-xy-x+xy^3-y^4##
Replies
5
Views
1K
I 2nd order ODE numerical solution
Replies
9
Views
3K

Hot Threads

Recent Insights

Back
Top