Community RSS Feed https://community.wolfram.com RSS Feed for Wolfram Community showing any discussions in tag Equation Solving sorted by active Dynamical Gravastars https://community.wolfram.com/groups/-/m/t/2820793 &amp;[Wolfram Notebook] : https://www.wolframcloud.com/obj/72ec4116-3e10-4c90-84f5-f364ca1e5314 Stephen Adler 2023-01-31T18:38:10Z Replacement of SymmetricGroupIndex result with input in second program https://community.wolfram.com/groups/-/m/t/2820364 I have Mathematica Home Edition 13.1 running on a Mac OS X Arm (64-bit) platform. The result of the first program appears in the denominator of the line in the second program beginning with &#034;X[y_] = &#034;. When I replace this denominator with the second input line of the first program, the program no longer works. I would like to combine these two programs into one, but apparently I don&#039;t have a good handle on the timing of the replacement. It seems to get deferred and then the program hangs. In = mc = 5; SymmetricGroupIndex[mc, x] /. x[i_] -&gt; If[i == 1, y, rp[i]] Out = y^5/120 + 1/12 y^3 rp + 1/8 y rp^2 + 1/6 y^2 rp + 1/6 rp rp + 1/4 y rp + rp/5 In = digits = 17; mc = 5; (* mc=maximum children *)m = 2 digits + 10; b[n_, i_, t_, k_] := b[n, i, t, k] = If[i &lt; 1, 0, Sum[Binomial[b[i - 1, i - 1, k, k] + j - 1, j]* b[n - i*j, i - 1, t - j, k], {j, 0, Min[t, n/i]}]]; b[0, i_, t_, k_] = 1; gf = 1 + Sum[b[j - 1, j - 1, mc, mc] x^j, {j, 1, m + 1}]; g[r_] := Module[{rp, X, ym}, For[k = 2, k &lt;= mc, k++, rp[k] = gf /. x -&gt; r^k]; X[y_] = (y - 1)/(y^5/120 + 1/12 y^3 rp + 1/8 y rp^2 + 1/6 y^2 rp + 1/6 rp rp + 1/4 y rp + rp/5); ym = y /. FindRoot[X&#039;[y] == 0, {y, 2}, WorkingPrecision -&gt; digits + 5]; X[ym]]; rho = FixedPoint[g, 1/3, SameTest -&gt; (Abs[#1 - #2] &lt; 10^-digits &amp;)]; RealDigits[rho, 10, digits] // First Out = {3, 4, 0, 0, 1, 7, 4, 6, 9, 1, 5, 1, 0, 6, 0, 0, 8} Robert Russell 2023-01-31T18:27:20Z Determine solution of an underdetermined linear equation system https://community.wolfram.com/groups/-/m/t/2820912 How can I get the same (i.e., a plane equation as) solution set of the linear system of equations in Mathematica as in Maple on the attached PDF (from a friend)? Thanks in advance Nina Teller 2023-01-31T16:42:11Z Studying hyperchaotic ﬁnance system https://community.wolfram.com/groups/-/m/t/2819693 &amp;[Wolfram Notebook] : https://www.wolframcloud.com/obj/c31f4ade-4c34-48ba-8018-63e7bb1efb44 Athanasios Paraskevopoulos 2023-01-30T09:19:15Z Solve error: not quantified system https://community.wolfram.com/groups/-/m/t/2819414 Hello, ![enter image description here] : https://community.wolfram.com//c/portal/getImageAttachment?filename=6193Capture.JPG&amp;userId=2803344 How can this system of 7 equations with 7 unknowns be solved in Wolfram Mathematica? is it possible to be solved this with Mathematica software? Wolfram Mathematica 12 Notebook file attached. Thank you. Cornel B. 2023-01-29T11:03:47Z Introduction to numerical methods: discretization of the continuous https://community.wolfram.com/groups/-/m/t/2816615 &amp;[Wolfram Notebook] : https://www.cup.gr/book/mathematica-ke-efarmoges/ : https://www.wolframcloud.com/obj/a4cba903-4b67-4552-9cf5-bb13918004e5 Athanasios Paraskevopoulos 2023-01-26T22:00:13Z DSolve vs Wolfram Alpha / hand calculation results https://community.wolfram.com/groups/-/m/t/2819025 I am trying to solve the following second order differential equation with constant coefficients df[x_[t_]] = 4* D[x[t], {t, 2 }] + 2* D[x[t], {t, 1 }] + 4* D[x[t], {t, 0 }] With the following inhomogeneity: ih[t_] = -9 E^(-t/4) Sin[t (Sqrt/4)] When I solve the equation by hand I get a general solution that looks like: sln = {{x -&gt; Function[{t}, (C*Cos[(Sqrt*t)/4])/ E^(t/4) + (C*Sin[(Sqrt*t)/4])/E^(t/4) + ((3/10)*(Sqrt*t*Cos[(Sqrt*t)/4] ))/E^(t/4)]}} The same solution is obtained by entering the equation into wolfram alpha and asking for a solution. However when using Dsolve to work out the solution: df1s = FullSimplify[DSolve[df[x[t]] == ih[t], x, t]] I obtain an extra term in the particular solution of the form ( after simplification) : 3/10 E^(-t/4) * -2*Sin[(Sqrt*t)/4] Substituting both answers back into the equation in Mathematica gives back the original inhomogeneity, Indicating that both solutions are &#034;correct&#034;. But as far as I can tell both terms are only equivalent when the extra sin term goes to 0. For example when t = 0. I have the following questions and would be very interested if anyone can shed some light on why this happens. 1 ) Why do Dsolve and wolfram alpha give different answers. Is it because wolfram alpha is not using a Dsolve like process but instead working out the example &#034;step by step&#034; as shown in the &#034;step by step&#034; solution provided. 2) Where is this extra term coming from ? Is it because Dsolve is &#034;solving&#034; the equation around a point like t=0 where both expressions are equivalent and thus can&#039;t distinguish the difference and just drags the extra term along as if it did not matter. 4) Why is substituting both terms back into the original differential equations in mathematica giving the same result. Are these two terms Truly equivalent even though they only seem to be equal at certain points ? 5) Is there anything that can be done to make Dsolve give the same answer as Mathematica or is it just a question of having to &#034;solve&#034; the problem step by step instead of using Dsolve to reach an answer. il attach a short notebook that shows the situation I am talking about. Please let me know if its not clear enough and I can make a neater example Thanks in advance. P.S: Giving DSolve the appropriate complex inhomogeneity and then extracting the imaginary part of the complex solution gives the exact same results. &amp;[Wolfram Notebook] : https://www.wolframcloud.com/obj/b9192c11-942e-4b28-b98e-cfe459cec803 Manuel Telleria 2023-01-28T20:23:56Z Overflow problem implementing Euler's method https://community.wolfram.com/groups/-/m/t/2817707 I tried to solve the following problem by the recursive method using the following code of the improved Euler&#039;s method, but it returns me a message &#039;&#039;Overflow occurred in computation&#039;&#039; $$X&#039;=Z+(Y-\alpha)X$$ $$Y&#039;=1-\beta Y-X^2$$ $$Z&#039;=-X-\gamma Z$$ with initial conditions $(X(0),Y(0),Z(0)=(1,2,3)$. Where X: interest rate Υ:investment demand Z: price index $\alpha$: savings, $\beta$: cost per investment, $\gamma$: the absolute value of the elasticity of demand I tried to solve by the recursive method using the following code of the improved Euler&#039;s method Q[a_, b_, h_, N_] := (u = a; v = b; Do[{u[n + 1] = u[n] + h* F[u[n] + (h/2)*F[u[n], v[n]], v[n] + (h/2)* G[u[n], v[ n]]], \ v[n + 1] = v[n] + h* G[u[n] + (h/2)*F[u[n], v[n]], v[n] + (h/2)*G[u[n], v[n]]]}, {n, 0, N}]) &amp;[Wolfram Notebook] : https://www.wolframcloud.com/obj/661c3ef2-4fe0-47d5-9d2e-85da3a0144cc Athanasios Paraskevopoulos 2023-01-27T10:36:59Z Two-level Rabi Problem-numerical solution https://community.wolfram.com/groups/-/m/t/2818584 Hello everyone! I want to numberically simulate the Rabi problem. It&#039;s basically to solve the following equations: ![the equations Rabi problem ] my code goes well when \[CapitalDelta]= 10^-4, \ \[CapitalGamma] = 10^4, but breaks down when the order difference goes higher. How to fix it? &amp;[Wolfram Notebook] : https://community.wolfram.com//c/portal/getImageAttachment?filename=%E5%B1%8F%E5%B9%95%E6%88%AA%E5%9B%BE_20230127_205446.png&amp;userId=2818537 : https://www.wolframcloud.com/obj/2dffb525-23d3-4ffd-bd4a-3dbf932f4a16 Wenxuan Xie 2023-01-28T01:59:19Z