I need a norm for the vector space of the solution set of the ODE y"=y?
88038
It's been too long, so I'm very rusty on this but you could look at Lp norm  ||f|| = pth Root of (integral( f^p)) where the integral is taken over the real line. Try L2.
931612
f^{-1}(y) = (y-42) / 7\ns
776599
http://www.purplemath.com/modules/fcns2.htm
962855
should be e^u*du/dx\n\nd[e^(x^2)] = e(x^2)*2*x
587075
Would be happy to help, but some information is missing.  I am assuming that you are asking about the region bounded by the following four equations:\n{2x + y < 25}  {x + y < ?}  {x < 12}  {x > 0}\n\nNeed to know what ? is in order to give an exact answer.
806655
dx=2xlny-2z\ndy=x^2*(1/y)-2z\ndz= x^2lny-2
1178962
To solve this it's a pretty straightforward application of Laplace transforms. You can do this question using convolutions as follows:\n\nFirst take the laplace transfom of the ODE:\n\nlet L{y(t)}(s) = Y(s) be the laplace transform of y(t).  Then we have:\ns^2(Y(s))  - 2s + 3Y(s) = 1/s^2 - (e^-s)/s\n\nrearranging we have Y(s) = (1/s^2 - e^-s/s + 2s) (1/(s^2+3)) = G(s) H(s) where G(s) = (1/s^2 - (e^-s)/s)  and H(s) =  (1/(s^2+3)) \n\nnow using the inverse laplace formula for the convolution of two functions:\n\ny(t) = L(^-1){Y(s)} = integral from 0 to t of (h(t-x)g(x)dx) + 2cos(sqrt(3)t)\n\n where h(t) = 1/sqrt(3) sin(sqrt(3)t) and g(t) = (t - u1(t))\n\nand the integral can be evaluated. \n\nSorry for the readability but I don't think yahoo answers can render math text properly. Also, as a note, this question would be far easier to solve using a partial fraction method rather than unecesarily using convolutions.
1062782
you should use matlab.
856026
Use the gas law\nPV=nRT
1177010
If the you have a local max/min at an interior point, , the partial derivatives must be zero.\nSince the sum of the second partials is zero, the point must be a saddle point, not a max/min.
356491
http://mathworld.wolfram.com/HarmonicSeries.html
1107625
I assume you are able to take partial derivatives. So take the partial derivatives that appear in the heat equation (you did look up the heat equation, right?) and plug them in to see if you get equality.\n\nSo, the partial derivative with respect to t is\n-lambda^2 k*u(x,t). This is the same as k times the second partial derivative with respect to x. Looks right to me!
493627
You can refer this book:\n\nDifferential equations : linear, nonlinear, ordinary, parial - A.C. King, J. Billingham, and S.R. Otto.
74552
these are data from end fixing of the structure you should introduce to solve the system of equations, otherwise you would get infinite solutions or (rigide body motion)-Good Luck
589794
Formulate stability of the system as a function of its energy. Now, one has to show that minimum energy translates into max stability on finding the derivatives.
758848
let y = x^x\nw = ln y = xlnx\nthen y = e^w\ndy/dx = e^w * dw/dx\ndw/dx = x(1/x) + lnx = 1+lnx\ndy/dx = (1+lnx)*x^x
699032
wx - x =\n\nx(w - 1)\n\n- - - - - - -s-