# 2nd

1. ### Need explanation on 2nd DE

Cannot find explanation for this : Why e^{rx} satisfies the equation yâ€™â€™+pyâ€™+qy=0 ? p,q-constants. How to prove it and how to derive it , where it comes from ? My thoughts are to substitute for y=\sum_{}^{\infty} c_n x^{n} and see the results. Method required !
2. ### Why 2nd formula of C.I is used?

Value of X, Ram invested Rs 6400 on compound interest at the rate of X% and gets an amount of Rs 8464 as interest after 2 yrs. Quantity II â†’ A/P = (1+ R/100)^n â†’ âˆš(8464/6400) = (1+ R/100)^n â†’ 23/20 = 1 + R/100 â†’ R = 15% There are C.I formulas: C.I = P([1 + R/100]^n â€“ 1); A = P...
3. ### GÃ¶del's 2nd theorem ends in paradox

Godel's 2nd theorem ends in paradox http://gamahucherpress.yellowgum.com/wp-content/uploads/GODEL5.pdf Godel's 2nd theorem is about "If an axiomatic system can be proven to be consistent and complete from within itself, then it is inconsistent.â€ But we have a paradox GÃ¶del...
4. ### Dynamics 2nd question

A ship is travelling at 24 km/h in the direction N60E. At noon it is 26 km due west of a ship which is travelling south at 24km/h. Find the nearest approach of the two ships and show that this occurs at approximately 12.21 p.m. If, at noon, the captain of P had decided to intercept Q, in what...
5. ### Elementary Linear Algebra 2nd Edition.

Hi! Please find this interesting Algebra book in the following link: https://smartmanmaths.com/2017/10/26/elementary-linear-algebra-2nd-edition/ What do you think about it?
6. ### Proving general solution for 2nd order ODE

Show that y(t) = A(t^2) + Bt, where A and B are arbitrary constants, is the general solution of the differential equation (t^2)yâ€²â€² âˆ’ 2t yâ€² + 2 y = 0. I got the roots to be r= (1/t)+-(i/t) .... Which I would then plug into the equation involving complex roots which is...
7. ### 2nd Order ODE Problem

I find 2nd Order ODEs quite hard and I've come across this question in my text book but am unsure of how to do it. Can anybody explain step by step how this is done? It would be a huge help considering I've an exam in a few weeks' time on this stuff. :o
8. ### 2nd order differential equation

Good afternoon all, I have a 2nd order diff equation as part of my first year math assignment. I seem to be getting nowwhere with it. m (d^2 h)/(dt^2 )+k dh/dt=-mg First part is turning it into a first order equation, where v=dh/dt. I have got d^2/dt^2 = -g -(k(v^2))/m I think that's the...
9. ### 2nd Order Diff-equation with spring mass dashpot system

A friend of mine asked me this and I am a bit stuck too. I figure this would be a good place to ask even though I haven't used this for a very long time A car's suspension system and springs and shock absorbers may be modeled as a spring-mass-dashpot system; irregularities in the road surface...
10. ### The 2nd Int'l Conference on Probability and Stochastic Analysis (ICPSA 2016)

The 2nd Int'l Conference on Probability and Stochastic Analysis (ICPSA 2016) The 2nd Int'l Conference on Probability and Stochastic Analysis 2016.7.25-27 Suzhou Topics Probability Theory / Theoretical Probability Infinite Dimensional Analysis Quantum Probability...
11. ### The 2nd Int'l Conference on Functional Analysis (ICFA 2016)

The 2nd Int'l Conference on Functional Analysis (ICFA 2016) The 2nd Int'l Conference on Functional Analysis 2016.7.25-27 Suzhou Topics HilbertSpaces BanachSpaces Banach-SteinhausTheorem Hahn-BanachTheorem OpenMappingTheorem ClosedGraphTheorem...
12. ### The 2nd Conference on Ordinary Differential Equations and Dynamical Systems (CODEDS 2

The 2nd Conference on Ordinary Differential Equations and Dynamical Systems (CODEDS 2016) The 2nd Conference on Ordinary Differential Equations and Dynamical Systems 2016.7.25-27 Suzhou Topics Theories of Ordinary Differential Equations (ODEs) Computational Ordinary...
13. ### The 2nd Int'l Conference on Groups and Algebras (ICGA 2016)

The 2nd Int'l Conference on Groups and Algebras (ICGA 2016) The 2nd Int'l Conference on Groups and Algebras 2016.7.25-27 Suzhou Topics Commutative/Non-Commutative Algebras Algebraic Number Theory Algebraic Geometry Linear Algebras and Matrix Ring and Homological...
14. ### The 2nd Int'l Conference on Partial Differential Equations (ICPDE 2016)

The 2nd Int'l Conference on Partial Differential Equations (ICPDE 2016) The 2nd Int'l Conference on Partial Differential Equations 2016.7.25-27 Suzhou Topics Hyperbolic Equations Elliptic and Parabolic Equations Equations of Mixed Type Conservation Laws Euler...
15. ### The 2nd Int'l Conference on Statistics and its Applications (iCSA 2016)

The 2nd Int'l Conference on Statistics and its Applications (iCSA 2016) 2016å¹´ç¬¬äºŒå±Šç»Ÿè®¡å­¦åŠåº”ç”¨å›½é™…å­¦æœ¯ç ”è®¨ä¼š Home - iCSA 2016 2016.7.25-27 Suzhou Topics Theoretical Statistics Mathematical Statistics Descriptive Statistics Inferential Statistics /...
16. ### 2nd Order diff (PLZ HELP ! :D)

How do i approach this question?? Imgur: The most awesome images on the Internet Imgur: The most awesome images on the Internet (it's not letting me embed the image so here are the links) I got a) as my" + By' =mg however can't solve for part b) Any help would be greatly appreciated!! Thank...
17. ### Reduction of 2nd order PDE to a first order equations system

I want to convert this linear second order general form PDE to two equations: $Ï•_{xx}+bÏ•_{xy}+cÏ•_{yy}+dÏ•_x+eÏ•_y+fÏ•=g(x,y)$ Converted equations: $a_1 u_x+b_1 u_y+c_1 v_x+d_1 v_y=f_1$ $a_2 u_x+b_2 u_y+c_2 v_x+d_2 v_y=f_2$ How can I do it? Hint: $Ï•_{xx}+Ï•_{yy}=0$ $u=Ï•_x , v=Ï•_y$...
18. ### 2nd God Particle

well Peter Higgs has discover the first god particle which provide mass to the objects. but there need to be a particle which must have the information about entropy. let me explain it in detail know that GRAVITY play a very very useful role in our universe, but at quantum level this...
19. ### pde ivp 2nd order wave equation

The analytical solution for this equation (âˆ‚^2 U)/(âˆ‚t^2 )+(âˆ‚^2 U)/âˆ‚tâˆ‚x-2 (âˆ‚^2 U)/(âˆ‚x^2 )=0 U(x,0)={(1-sin(x)x,|x|<1 0 otherwise) Assuming sin(x) =-1, x<0, 1, x>0 ã€–âˆ‚U/âˆ‚tã€—_(t=0)={(cos(Ï€x),|xâ”‚<1 0 otherwise)
20. ### Inverse Laplace Transform of a 2nd Order ODE

23.) y'' +2y' + y = 4 e^-t; y(0) = 2, y'(0) = -1 My attempt: a = 1, b = 2, c = 1 F(s) = 4 L( e ^ -t) = 4/(s + 1) (Taken from Laplace Transform Table) Y(s) = [(as + b) y(0) + a y'(0) + F(s)]/(as^2 + bs + c) Plugging and Simplifying: Y(s) = (2s^2 + 5s + 7)/[(s + 1)(s^2 + 2s +...