## ODE non linear first order...

Dear all,

I would like to solve the following non linear ODE with Maple, but I am no able. I do not know if it is possible, beccause it is nolinear.

I really appreciate any advice or help. This is the equation:

y'(x) - (Q - x*p0*(exp(alpha-beta*y(x)))/(1+exp(alpha-beta*y(x))))^2=0

thanks a lot

## Getting a smooth DEplot3d from a stiff system of e...

I've been trying to make a smooth plot of some ODEs. It should show C rapidly increasing at the innitiation, until they get into a quassi steady state,  and then all three variables increase much slower. This should look like a roughly straight line that elbows sharply into a smooth curve.

Any attempt to DEplot3d it i've made either just shows the time before the quassi steady state is reached, so shows the straight line; or smooths that time together with the next period, making the straight line look like a part of the smooth curve.

Model := [diff(B[1](t), t) = k[a1]*C(t)*(R-B[1](t)-B[2](t))-k[d1]*B[1](t), diff(B[2](t), t) = k[a2]*C(t)*(R-B[1](t)-B[2](t))-k[d2]*B[2](t), diff(C(t), t) = (-(k[a1]+k[a2])*C(t)*(R-B[1](t)-B[2](t))+k[d1]*B[1]+k[d2]*B[2](t)+k[m]*((I)(t)-C(t)))/h];
DissMod := subs((I)(t) = 0, Model);
AssMod := subs((I)(t) = C[T], Model);

Pars := [k[a1] = 6*10^(-4), k[d1] = 7*10^(-3), k[a2] = 5*10^(-4), k[d2] = 10^(-2), R = .5, k[m] = 10^(-4), C[T] = 100, h = 10^(-6)]

StateSol := DEplot3d(subs(Pars, AssMod), [B[1](t), B[2](t), C(t)], t = 0 .. 1000, number = 3, B[1] = 0 .. .5, B[2] = 0 .. .5, [[B[1](0) = 0, B[2](0) = 0, C(0) = 0]], scene = [B[1](t), B[2](t), C(t)], maxstep = .1, maxfun = 0, method = l)

## Default method??...

Hello all..

Im sharena and i am solving ODE BVP by using maple. i used this command to solved the equation..

However, i dont know which method this programm solved my ODE. Is it RK45 method??

## Adomian Decomposition Method...

pls help review this code, its doesnt return a solution

restart;
Digits := 16;
M := .5; lambda := .5; Pr := .72; beta := 1; L[w] := 0; m := 1; R := 1; Ec := 1;
N := 7;
for j from 0 to N do J[j] := sum(f[k](t)*(diff(f[j-k](t), `\$`(t, 2))), k = 0 .. j) end do;
for i from 0 to N do K[i] := sum((diff(f[k](t), t))*(diff(f[i-k](t), t)), k = 0 .. i) end do;
for j from 0 to N do G[j] := sum(f[k](t)*(diff(theta[j-k](t), t)), k = 0 .. j) end do;
for j from 0 to N do H[j] := sum((diff(f[k](t), t))*theta[j-k](t), k = 0 .. j) end do;
for i from 0 to N do P[i] := sum((diff(f[k](t), t, t))*(diff(f[i-k](t), t)), k = 0 .. i) end do;
epsilon := 1; delta := 0;
f[0] := proc (t) options operator, arrow; L[w]+epsilon+delta*A*t+(1/2)*A*t^2 end proc;
1 2
t -> L[w] + epsilon + delta A t + - A t
2
theta[0] := proc (t) options operator, arrow; 1+B*t end proc;
t -> 1 + B t
NULL;
;
NULL;
NULL;
NULL;
NULL;
for i to N do f[i] := simplify(-((m+1)*(1/2))*(int(int(int(J[i-1], t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))+m*(int(int(int(1-K[i-1], t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))-M*(int(int(int(diff(f[i-1](t), t)-1, t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))-lambda*(int(int(int(theta[i-1](t), t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))); f[i] := unapply(f[i], eta); theta[i] := simplify(-3*Pr*R*(((m+1)*(1/2))*(int(int(G[i-1], t = 0 .. eta), t = 0 .. eta))-(2*m-1)*(int(int(H[i-1], t = 0 .. eta), t = 0 .. eta))+Ec*(int(int(P[i-1], t = 0 .. eta), t = 0 .. eta)))/(4+3*R)); theta[i] := unapply(theta[i], eta) end do;
NULL;
F(eta):=collect((&sum;)f[z](eta),eta):
Theta(eta):=collect((&sum;)theta[z](eta),eta):
with(numapprox);
for k from 2 to 5 do W[k] := pade(diff(F(eta), eta), eta, [k, k]); Q[k] := pade(Theta(eta), eta, [k, k]); SOLL1[k] := expand(coeff(numer(W[k]), eta^k)) = 1; SOLL2[k] := expand(coeff(numer(Q[k]), eta^k)) = 0; SOL[k] := solve({SOLL1[k], SOLL2[k]}, {A, B}); print([k] = SOL[k]) end do;
Warning, computation interrupted

## BVP Ode ,how can tackle derivative involve in bcs...

how i tackle an bvp ode,derivative involve in bcs.i want to solve by dsolve comand or by using Rk meethod.i am attaching the maple sheet,ode wrrten in attached maple sheet

thank you

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## Error, (in dsolve/numeric/bvp) system is singular ...

i have problem on running the ode bcs

there is cos n sine in ther ode

any idea to solve this ?

i have attched it

thnks
Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/Sc.mw .

## Can Maple determine this ODE's initial value?...

Can Maple determine the value of DthetaZero such that the solution to the ODE, for some specific value of t, simultaneously provides the two values theta(t)=Pi and diff(theta(t),t)=0?

sol:=dsolve({4*sin(theta(t))*cos(theta(t))-9.8100*sin(theta(t))-(diff(theta(t), t, t)) = 0, theta(0) = 2*Pi*(1/3), D(theta)(0) = DthetaZero}, numeric)

odeplot(sol,[t,theta(t),diff(theta(t),t)],t=0..5) for trial values of DthetaZero shows that the desired value is

1.0340*Pi <DthetaZero<1.0345*Pi.

## solution for ode and how to tackle constant ...

how we can solve an ode with exat soltuion n calculate the unknw constant which aries after solving an ode.???