Hello everybody

can anybody help me solve this differential equation please?

d^2y(t)/dt^2-dy(t)/dt*1/y(t)=a*y(t)^2

I am really not good at writing the code. The code was from the book (Stochastic process with maple).

It does not seem to generate the different plots when I run the code.

Also the last added code was from the book but it shows error.

Thank you for the help in advance. (My English also is not good.)
 

Download randomWalk.mw
 

Download randomWalk.mw

Could you help me?

Download randomWalk.mw
 

Download randomWalk.mw

restart; with(stats); with(plots); RandWalk :=proc(N,p,q,sa,sb,M) local A,B,r,PA,PC,PB, state,step,path: A:=-N: B:=N: r:=1-p-q: PA:=empirical[0.,sa,1-sa]: PC:= empirical[q,r,p]: PB := empirical[1-sb,sb,0.]: state:=0: path:=state: from 1 to M do if (A< state and state

with(LinearAlgebra):
assign(seq(U || i = `<,>`(x[i], y[i]), i = 1 .. 3));
U || 4 := U || 1; r := (1/6)*sqrt(3);
assign(seq(V || i = (U || i+U || (i+1))*(1/2)+(`<,>`(`<|>`(0, 1), `<|>`(-1, 0)) . (U || (i+1)-U || i))*r, i = 1 .. 3)); Norm(V || 3-V || 1, 2); is(Norm(V || 3-V || 1, 2) = Norm(V || 3-V || 2, 2)); is(Norm(V || 2-V || 1, 2) = Norm(V || 3-V || 2, 2));

Starting from 3 points of a base, then got 3 lines equations.

If having 3 lines equations of a cone surface, how to find the surface equation of a cone?

I find many tools about differential 

i had some differential ideal

how to use these tools to research what application can be applied with differential ideals I discovered?

Given a list of numeric value lists, calculate the average of each sub-data list

### I am writing a code for an Optimal control using pontryagins maximum principle. I have supplied all neccessary boundary conditions yet it fails to detect one of the conditions. It gives an error message whenever I run it.

I need guidance. Thank you

restart;
with(plots);
r := 3; r[1] := 3; k := 10; a := 0.2e-1; b := 0.1e-1; c := 0.1e-1; beta := 0.3e-1; alpha := 0.3e-1; m := 0.5e-1;
z := 40; q := 5; p := 100; T := 3;
sigma := 0.1e-1; k[1] := 10; rho := 0.5e-1;

u[1] := min(max(0, z), 1); z := (a*m*k*lambda[2](t)*x(t)*y(t)-lambda[1](t)*r*(1+b*x(t)+c*y(t))*x(t)*x(t))/(z*k*(1+b*x(t)+c*y(t))); u[2] := min(max(0, q), 1); q := -lambda[1](t)*beta*x(t)*s(t)/q; u[3] := min(max(0, p), 1); p := -(r[1]*lambda[3](t)*s(t)*s(t))/(p*k[1]);
NULL;
sys := diff(x(t), t) = r*x(t)*(1-(1-u[1])*x(t)/k)-a*m*x(t)*y(t)/(1+b*x(t)+c*y(t))-beta*(1-u[2])*x(t)*s(t), diff(y(t), t) = -alpha*y(t)+a*m*x(t)*y(t)/(1+b*x(t)+c*y(t)), diff(s(t), t) = sigma*s(t)+r[1]*s(t)*(1-(1-u[3])*s(t)/k[1])-rho*s(t)*y(t), diff(lambda[1](t), t) = -lambda[1](t)*(r-2*r*(1-u[1])*x(t)/k-a*y(t)*(1+c*y(t))/((1+b*x(t)+c*y(t)) . (1+b*x(t)+c*y(t)))-beta*(1-u[2])*s(t))-lambda[2](t)*a*m*(1-u[1])*(1+c*y(t))*y(t)/((1+b*x(t)+c*y(t)) . (1+b*x(t)+c*y(t))), diff(lambda[2](t), t) = -lambda[1](t)*a*x(t)*(1+b*x(t))/((1+b*x(t)+c*y(t))*(1+b*x(t)+c*y(t)))+lambda[2](t) . (-alpha+(a*m*(1-u[1]) . (1+b*x(t)))*x(t)/((1+b*x(t)+c*y(t))*(1+b*x(t)+c*y(t))))+lambda[3](t)*rho*s(t), diff(lambda[3](t), t) = lambda[1](t)*beta*(1-u[2])*x(t)-lambda[1](t)*(r[1]-2*r[1]*(1-u[3])*s(t)/k[1]-sigma-rho*y(t)), x(0) = 10, y(0) = 20, s(0) = 10, lambda[1](T) = 0, lambda[2](T) = 0, lambda[3](T) = 0;
p1 := dsolve({sys}, type = numeric, method = bvp[midrich], abserr = .1);
Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 7, got 6
p2o := odeplot(p1, [t, y(t)], 0 .. 2, numpoints = 100, labels = ["Time (months)", " "*`badbiomass""spatina"""`], labeldirections = [horizontal, vertical], style = line, color = red, axes = boxed);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution
r := 3; r[1] := 3; k := 10; a := 0.2e-1; b := 0.1e-1; c := 0.1e-1; beta := 0.3e-1; alpha := 0.3e-1; m := 0.5e-1; sigma := 0.1e-1; k[1] := 10; rho := 0.5e-1;
z := 40; q := 5; p := 100; T := 3;

fun := diff(x(t), t) = r*x(t)*(1-x(t)/k)-a*m*x(t)*y(t)/(1+b*x(t)+c*y(t))-beta*x(t)*s(t), diff(y(t), t) = -alpha*y(t)+a*m*x(t)*y(t)/(1+b*x(t)+c*y(t)), diff(s(t), t) = sigma*s(t)+r[1]*s(t)*(1-s(t)/k[1])-rho*s(t)*y(t), x(0) = 10, y(0) = 20, s(0) = 10;
p2 := dsolve({fun}, type = numeric);
Error, (in f) unable to store 'HFloat(10.0)*r*(1-HFloat(10.0)/k)-HFloat(3.1538461538461537)' when datatype=float[8]
p2i := odeplot(p2, [t, y(t)], 0 .. 2, numpoints = 100, labels = ["Time(months)", " bad biomass"], labeldirections = [horizontal, vertical], style = line, axes = boxed, color = blue);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution
plots[display](p2i, p2o);
Error, (in plots:-display) expecting plot structure but received: p2i

do math regex solver exist in this world?

expect to output a set of regex for pattern

and then use regex to generate condition or rules equations and then use sorting algorithm to find whether match all data

Hello!

How can I print steps of ReducedRowEchelonForm when i got martix with dimensions 6x7(augmented)?

With command Expand Steps occurs an error: 

ExpandSteps(ReducedRowEchelonForm(macierzA))

In Maple 2019 it is not possible to change to "1-D Math Input".

But it is possible to convert (right mouse->convert to-> 1D Math Input)

In this mode I get the following results:

I have not touched Maple in about 10 years and I'm back but apparently my Maple skills got quite a bit it rusty. I'm trying to plot a function but keep getting this warning and a blank graph:

"Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct"

Here is what I'm trying to do (put and call formulas for Black 76 model):

> with(Statistics);
> X := RandomVariable(Normal(0, 1));
> K := 150;
> r := 0.25e-1;
> s := .75;
> t := .5;
> d1 := f-> (log(f/K)+.5*s^2*t)/(s*sqrt(t)):

> d2 := f-> d1(f)-s*sqrt(t):
> c := f-> exp(-r*t)*(f*([CDF])(X, d1(f))-K*([CDF])(X, d2(f))) :
p := ->exp(-r*t)*(K*([CDF])(X, -d2(f))-f*([CDF])(X, -d1(f))):

All of the above work as intented:
> evalf(c(100)), evalf(p(100));

return the correct values. But I can't plot c( ) or p( ):

plot(c(f), f = 50 .. 100)

"Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct"

What am I doing wrong here? I will appreciate any help.

Thank you.

Fsolve produces the correct solution.  solve followed by evalf produces a completely different solution.

What am I doing wrong?

## Ioannes Colla problem: "Divide 10 into three parts such that they
## shall be in continued proportion and that the product of the first
## two shall be 6"
eqs := [a+b+c=10, a/b=b/c, a*b=6];
fsolve(eqs); ## correct solution
evalf(solve(eqs)); ## different

Tom Dean

If A is an m × n matrix and B is a p × q matrix, then the Kronecker product C = A ⊗ B is the mp × nq block matrix. Assume I have matrix C and want to find matrix A and B. This problem has known solution called "Nearest Kronecker Product". So I just need a function like this: A,B:=NearestKroneckerProduct(C)  which minimizes ||C - A ⊗ B||_F  where F denotes frobenius norm. 

Here is an Image that shows a mathematica code:

I took it from the link below:

https://mathematica.stackexchange.com/questions/91651/nearest-kronecker-product

Also there is a matlab code:

https://gist.github.com/tholden/58dd9a8991daa750ae36a633fe7060a4/revisions

can you convert mathematica code to maple?