## Solve Differential Equation with Boundary Conditions (lengthy equation)

I have a lengthy equation to be substitute into a differential equation. I used DSolve to generate the output. However, it took me more than 3 hours and it still running. The DE is the convective-diffusion equation which is

1/r del /del r (r del f1s/ del r) - a1 = 0

and the boundary condition is r=k when del f1s/ del r =0

so the input is:

a1 = -(810165067720210957064125/25546163167349695028752149) -       0.00395833 (-0.5 + r) (1.02817 +          3.98107/(5.36839*10^11/r - 1.*10^12 r)^(1/20) +          2./((1.27718 - 0.666667 r - 0.333333 r^2)/(1. + r))^(1/20) +          3./((3.05377 - 0.888889 r - 0.111111 r^2)/(4. + r))^(1/20) +          3.01772/(-((1. (-0.675531 + 0.125 r + r^2))/(0.0625 + r)))^(         1/20) + 3.03794/(-((1. (-0.867019 + 0.285714 r + r^2))/(           0.142857 + r)))^(1/20) +          2.04096/(-((1. (-1.14539 + 0.5 r + r^2))/(0.25 + r)))^(1/20) +          3.08948/(-((1. (-1.57936 + 0.8 r + r^2))/(0.4 + r)))^(1/20) +          3.12414/(-((1. (-2.32712 + 1.25 r + r^2))/(0.625 + r)))^(1/20) +          3.23431/(-((1. (-7.80849 + 3.5 r + r^2))/(1.75 + r)))^(1/20)) +       0.125 (-0.5 + r) (0.196614 +          1.32702*10^-12 (5.36839*10^11/r - 1.*10^12 r)^(19/20) +          0.666667 ((1.27718 - 0.666667 r - 0.333333 r^2)/(1. + r))^(          19/20) + ((3.05377 - 0.888889 r - 0.111111 r^2)/(4. + r))^(         19/20) +          0.894139 (-((1. (-0.675531 + 0.125 r + r^2))/(0.0625 + r)))^(          19/20) +          0.787613 (-((1. (-0.867019 + 0.285714 r + r^2))/(0.142857 + r)))^(          19/20) +          0.453547 (-((1. (-1.14539 + 0.5 r + r^2))/(0.25 + r)))^(19/20) +          0.572125 (-((1. (-1.57936 + 0.8 r + r^2))/(0.4 + r)))^(19/20) +          0.462835 (-((1. (-2.32712 + 1.25 r + r^2))/(0.625 + r)))^(          19/20) +          0.239579 (-((1. (-7.80849 + 3.5 r + r^2))/(1.75 + r)))^(19/20))   TRY = DSolve[{1/r D[r f1s'[r], r] - a1 == 0, f1s'[k] == 0}, f1s, r, GeneratedParameters -> S] 

I’m stuck and I don’t know what else should I do. I tried to do manually by integrating the equation but it’s kinda haywire. Could anyone help me out with this coding. Really appreciate it 🙂

## How can I solve this PDE?

I got the following equation from physics.

$$C \sin \theta \frac{\partial T}{\partial \theta} = \frac{1}{r} \frac{\partial }{\partial r} \left( r \frac{\partial T}{\partial r} \right)$$ where boundary conditions are

$$T=T_w$$ for $$r,

$$T=T_0$$ where $$r \rightarrow\infty$$,

and $$C, T_0, T_w, r_0$$ are constant.

(Symmetrical for all $$\theta$$)

I would like to find $$\frac{\partial T}{\partial r}$$ where $$r=r_0$$ from the equation.

How can I solve using Mathematica? Thank you so much!

## Solving a complex equation with Solve

I would like to solve:

$$e^{-b (1.365)} + e^{-b(-0.350)} + e^{-b(-0.378)} = 0$$, where $$b$$ is complex.

So, I have written:

Solve[{E^((-b1 - I b2) (1.365)) + E^((-b1 - I b2) (-0.350)) + E^((-b1 - I b2) (-0.378)) == 0, {b1, b2} \[Element] Reals}, {b1,b2}] 

which returns a huge list. How can I get a exact answer? And if it has many solutions, is it possible that I plot the solution points altogether in the complex plane?

## How do you install and solve the configure step from source in grid db?

I am running Ubuntu 18 and the error following installation instructions persists

### 2nd Query

INSERT INTO foldertable(     serverToken,     folderName,     folderid,     RootFolderPath,     createdTime,     LastEdited,     RootFolderPreviewPath,     userFolderPathName,     starred,     trashed ) VALUES(     1235465,     '',     'ABCEfghi',     '',     '',     '',     '',     '',     '',     '' ); 

### Result

1 row inserted. (Query took 0.0087 seconds.)

I am quite new to mysql . I am using xampp for Testing and phpmyadmin for query and postman for transaction api .

So How can I solve this strange behaviour .

## How to Solve Functional Differential Equation

I tried to solve this equation numerically.

eqnEx = x''[t] + x[2 t] == 0; NDSolve[{eqnEx, x[1] == 10, x'[1] == 0}, x[t], {t, 1, 10}] 

Two important character of the equation are that function variable is 2t and initial condition is given at t=1 .

After Calculation, Mathematica gives this error message

NDSolve : The method currently implemented for delay differential equations does not support delays that depend directly on the time variable or dependent variables 

After google, I find these kind of equation are called Functional Differential Equation and I could not obtain how to solve it. Is there a way to solve these kind of equation numerically?

## How can i solve php upgrade problem

I am using a plugin that works on Woocommerce.
While no error occurs on PHP 7.2 (eg 7.3) I get an error like the following in 7.2. The developer team is not helping. How can I resolve this error? It is probably caused by a foreach loop defined in the plugin. However, I am not sure how to find this cycle. I’ve been researching for about a week. I could not find a solution. I looked at a change that came with new versions of PHP. I could not see any change regarding the foreach loop. I searched for similar problem on other platforms. Unfortunately, I could not find it.

invalid argument supplied for foreach() in woocommerce/includes/wc-template-function.php on line 2735.

## Getting Mathematica to solve a system of two second order nonlinear ordinary differential equations

I tried solving a system of two second order nonlinear ordinary differential equations using the DSolve command. First, I tried like this:

eqns = {A''[x] == 2/B[x]*A'[x]*B'[x],     B''[x] + 1/B[x]*(A'[x])^2 - 1/B[x]*(B'[x])^2 == 0}; sol = DSolve[eqns, {A, B}, x] 

However, as Mathematica didn’t (couldn’t?) solve this, I transformed it into a system of four first order equations:

eqns = {c'[x] == 2/B[x]*c[x]*d[x],     d'[x] + 1/B[x]*(c[x])^2 - 1/B[x]*(d[x])^2 == 0, c[x] == A'[x],     d[x] == B'[x], c[0] == 1, d[0] == 1, A[0] == 1, B[0] == 1}; sol = DSolve[eqns, {A, B, c, d}, x] `

This still doesn’t work. Weirdly enough, I don’t even get an error message.

I only included the boundary conditions thinking that they may be helpful, but they aren’t part of my original problem.

Your help would be greatly appreciated:)