I'm looking for the general solution to the attached differential equation. Maple doesn't provide it. What am I doing wrong?

Download testdgl5.mw

this transforamtion including two function which i try to do, but my result is so different and even is not near i did like the author mention but i don't know how reach that outcome, the importan part is the equation 2.7

s1.mw

in here i want to apply this method for finding my parameter but is a special kind of substituion and i don't know how hundle this kind  and find the parameters i did some part but i didn't reach the target 

f-p-second.mw

almost i did all the case but some case i determined in red color are not satisfy what is problem of them and how i can apply the case 47-52, beside this i changed the ode in eq(15) i didn't write rho parameter  is make any problem?

ode-17.mw

 i wait 30 minute to  see the result of this function it will zero or not but is not give me outcome, is so importan for me which to see this function is my answer, how i can see the result, can  anyone give me the way 

T-pde.mw

Dear all,
I am trying to build an animated activity to introduce the concept of a definite integral.
My goal is to animate the graph simultaneously with a three-column table displaying the values of the upper Riemann sum, the lower Riemann sum, and the definite integral.
Any ideas or suggestions on how to implement this?
Many thanks in advance.

Riemann_Anim_table.mw

i found the same as author found but is not give me zero when i replace in my pdes can anyone see the problem?

test.mw

i try to find the parameter in this equation but some issues show up which i am not sure i can fix that or not? there is any way for finding thus parameters?

test-F-p.mw

i did my try to sketch the best shape of graph by existing code but the 3D shape in matlab is not what i am looking and is  not intresting for this kind of plot so i want use and design a better shape of 3D plot for thus contour  i need help for that 

plot-help.mw

i did try and even replace the function w(t) by anotehr thing but is not working  how i can find that and make be answer of my pde?

k1.mw

How can find thus parameters 

Dr.D-problem.mw

a million time i try to figure out how i can get this plot ? why my graph  in countor is not same the 3D plot? where is problem?

Bgraph1.mw

When I use latex(expression) to convert my expression to latex, the latex output is missing a large portion of my expression. See attached maplesheet. I want latex( ) to output the complete expression. What is happening

incomplete_latex_output.mw

restart;
with(plots): Digits:= trunc(evalhf(Digits)); #generally a very efficient setting

# Here we solve a 1D problem in 3 regions. In each region, we have concentration and potential (c,phi) distributions,
# We first solve the unperturbed steady-state problem and then the linearized perturbation problem (which rely on the steady state).
# Each region is defined in x = 0..1, and the regions are connected by interface conditions that connect (c1(1),phi1(1)) to (c2(0),phi2(0))  and (c2(1),phi2(1)) to (c3(0),phi3(0))

Q:=10;   omega:=100;     J0:= 1.95;   # parameters

# The unperturbed steady-state

c1:=1-J0/2*x:               c3:=1-J0/2*(x-1):                   # concentration distributions in region 1 and 3    
c12:= eval(c1,x=1):        c32 := eval(c3,x=0):  
T1:=sqrt(Q^2+4*c12^2):     T3:=sqrt(Q^2+4*c32^2):           # the values of concentrations 1 and 3 at the interfaces with region 2
c21:=(T1-Q)/2:             c23:=(T3-Q)/2:                     # the values of concentration 2 at the interfaces with region 1 and 3 
I0:=fsolve(Q*i0/2/J0*ln((J0*T1-Q*i0)/(J0*T3-Q*i0))=(J0-T1+T3)/2,i0);   # the electrical current 
V:=(I0/J0+1)*ln(c32/c12)+ln((c21+Q)/(c23+Q))+(J0+2*c23-2*c21)/Q;     # the potential drop across the system 
c2:=solve(y-c21+Q*I0/2/J0*ln((Q*I0-Q*J0-2*J0*y)/(Q*I0-Q*J0-2*J0*c21))=-J0/2*x,y):  # concentration distribution in region 2 
phi1:=I0/J0*ln(c1)+V:   phi3:=I0/J0*ln(c3):                         # potential distribution in regions 1 and 3    
phi21:=I0/J0*ln(c12)+V-0.5*ln((c21+Q)/c21):    
phi2:=(2*c21-2*c2+Q*phi21-J0*x)/Q:      # potential distribution in region 2    

# The linearized problem 
# Unknowns: C11,C12,Phi11,Phi12,C21,C22,Phi21,Phi22,C31,C32,Phi31,Phi32,sigma1,sigma2 (sigma1 and sigma2 are constants along x)

#   Equations

# Region 1 Equations 

eq11 := omega*C11(x)-diff(diff(C12(x), x), x) = 0:                            
eqA1 := 2*c1*diff(Phi11(x), x)+2*(diff(phi1, x))*C11(x) = -sigma1: 
eq12 := omega*C12(x)+diff(diff(C11(x), x), x) = 0:                          
eqA2 := 2*c1*diff(Phi12(x), x)+2*(diff(phi1, x))*C12(x)=-sigma2:

 # Region 2 Equations 

eq21 := omega*C21(x)-diff(diff(C22(x), x)+Q/2*diff(Phi22(x), x), x)=0:      
eqB1 := 2*(c2+Q)*diff(Phi21(x), x)+2*(diff(phi2, x))*C21(x)=-sigma1:
eq22 :=  omega*C22(x)+diff(diff(C21(x), x)+Q/2*diff(Phi21(x), x), x) = 0:  
eqB2 := 2*(c2+Q)*diff(Phi22(x), x)+2*(diff(phi2, x))*C22(x)=-sigma2:

# Region 3 Equations 

eq31 := omega*C31(x)-diff(diff(C32(x), x), x)=0:                            
eqC1 := 2*c3*diff(Phi31(x), x)+2*(diff(phi3, x))*C31(x)=-sigma1:
eq32 := omega*C32(x)+diff(diff(C31(x), x), x) = 0:   
eqC2 := 2*c3*diff(Phi32(x), x)+2*(diff(phi3, x))*C32(x)=-sigma2:

EqSys := eq11, eq12, eq21, eq22, eq31, eq32, eqA1, eqA2, eqB1, eqB2, eqC1, eqC2;    # Equations system 

# Boundary conditions 

# Bcs at the outer ends of regions 1 and 3
Bc1 := C11(0) = 0, C12(0) = 0,  C31(1) = 0, C32(1) = 0, Phi11(0)=1, Phi12(0)=0, Phi31(1)=0, Phi32(1)=0:

# ECP continuity at the two interfaces (between region 1 and 2 and between 2 and 3) 
Intf1 := Phi21(0)-Phi11(1)=C11(1)/(eval(c1, x = 1))-C21(0)/(eval(c2, x = 0)+Q),
Phi22(0)-Phi12(1)=C12(1)/(eval(c1, x = 1))-C22(0)/(eval(c2, x = 0)+Q),
Phi21(0)-Phi11(1)=C21(0)/(eval(c2, x = 0))-C11(1)/(eval(c1, x = 1)),
Phi22(0)-Phi12(1)=C22(0)/(eval(c2, x = 0))-C12(1)/(eval(c1, x = 1)),
Phi21(1)-Phi31(0)=C31(0)/(eval(c3, x = 0))-C21(1)/(eval(c2, x = 1)+Q),
Phi22(1)-Phi32(0)=C32(0)/(eval(c3, x = 0))-C22(1)/(eval(c2, x = 1)+Q),
Phi21(1)-Phi31(0)=C21(1)/(eval(c2, x = 1))-C31(0)/(eval(c3, x = 0)),
Phi22(1)-Phi32(0)=C22(1)/(eval(c2, x = 1))-C32(0)/(eval(c3, x = 0)):

# Fluxes  continuity at the two interfaces (between region 1 and 2 and between 2 and 3)
Intf2 := (Q*sigma1+2*Q*D(phi2)(0)*C21(0))/(2*eval(c2, x = 0)+Q) = 2*D(C21)(0)-2*D(C11)(1),
(Q*sigma2+2*Q*D(phi2)(0)*C22(0))/(2*eval(c2, x = 0)+Q) = 2*D(C22)(0)-2*D(C12)(1),
(Q*sigma1+2*Q*D(phi2)(1)*C21(1))/(2*eval(c2, x = 1)+Q) = 2*D(C21)(1)-2*D(C31)(0),
(Q*sigma2+2*Q*D(phi2)(1)*C22(1))/(2*eval(c2, x = 1)+Q) = 2*D(C22)(1)-2*D(C32)(0): 

Bc := Bc1,Intf1,Intf2;

sys := {EqSys,Bc}:

sol1 := dsolve(sys, numeric, method=bvp[midrich],output = procedurelist);
Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system
Sigma1 := subs(sol1, sigma1);
Sigma2 := subs(sol1, sigma2);
Cond := Sigma1(0)+I*Sigma2(0);
ZR := Re(1/Cond);
ZI := Im(1/Cond);
X:=ZR,-ZI;

is work for some equation but sometime is make problem and again make it problem for me where is problem why the denominator of second equation still remain while i want to remove it i times by denominator but still not worked

in my orginal ode i did change the place diff(V(xi),xi)=Omega(xi) maybe make problem ...or not

like this equation but the equation is different

Download make_system.mw