I have three coupled second order ODE's given as below

$x''[t] = -c_1*y'[t]-c_2*z[t]-c_3$
$y''[t] = -c_4*x'[t]$
$z''[t] = \frac{c_5}{c_6}*x[t]-c_6$

where $c_i$'s are know constants. The boundary conditions are

$x[-1]=x[1]=y[-1]=y[1]=z'[-1]=z'[1]=0$.

I followed the example given here How do I solve coupled ordinary differential equations?

{x, y, z} = {x, y, z} /. Dsolve[{x''[t] == -c1*y'[t] - c2*z[t] - c3, y''[t] == -c4*x'[t], z''[t] == -c5 + c5*x[t]/c6, x[-1] == 0, x[1] == 0, y[-1] == 0, y[1] == 0, z'[-1] == 0, z'[1] == 0}, {x, y, z}, t] // FullySimplify // First 

I get the following output

ReplaceAll::reps: {Dsolve[{x''[t] == -c3 - c2 z[t] - c1 y'[t], <<8>>}, {x, y, z}, t]} 

 is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. 

Set::shape: Lists {x, y, z} and {x, y, z} /. Dsolve[{x''[t] == 

-c3 - c2 z[t] - c1 y'[t], <<8>>}, {x, y, z}, t] are not the same shape. 

Could someone please tell me what is wrong with my approach and please suggest me how to solve this system.
Thank you for your time

I have three coupled second order ODE's given as below

$x''[t] = -c_1*y'[t]-c_2*z[t]-c_3$
$y''[t] = -c_4*x'[t]$
$z''[t] = \frac{c_5}{c_6}*x[t]-c_6$

where $c_i$'s are know constants. The boundary conditions are

$x[-1]=x[1]=y[-1]=y[1]=z'[-1]=z'[1]=0$.

I followed the example given here How do I solve coupled ordinary differential equations?

{x, y, z} = {x, y, z} /. Dsolve[{x''[t] == -c1*y'[t] - c2*z[t] - c3, y''[t] == -c4*x'[t], z''[t] == -c5 + c5*x[t]/c6, x[-1] == 0, x[1] == 0, y[-1] == 0, y[1] == 0, z'[-1] == 0, z'[1] == 0}, {x, y, z}, t] // FullySimplify // First 

I get the following output

ReplaceAll::reps: {Dsolve[{x''[t] == -c3 - c2 z[t] - c1 y'[t], <<8>>}, {x, y, z}, t]} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. 

Set::shape: Lists {x, y, z} and {x, y, z} /. Dsolve[{x''[t] == -c3 - c2 z[t] - c1 y'[t], <<8>>}, {x, y, z}, t] are not the same shape. 

Could someone please tell me what is wrong with my approach and please suggest me how to solve this system.
Thank you for your time

I have three coupled second order ODE's given as below

$x''[t] = -c_1*y'[t]-c_2*z[t]-c_3$
$y''[t] = -c_4*x'[t]$
$z''[t] = \frac{c_5}{c_6}*x[t]-c_6$

where $c_i$'s are know constants. The boundary conditions are

$x[-1]=x[1]=y[-1]=y[1]=z'[-1]=z'[1]=0$.

I followed the example given here How do I solve coupled ordinary differential equations?

{x, y, z} = {x, y, z} /. Dsolve[{x''[t] == -c1*y'[t] - c2*z[t] - c3, y''[t] == -c4*x'[t], z''[t] == -c5 + c5*x[t]/c6, x[-1] == 0, x[1] == 0, y[-1] == 0, y[1] == 0, z'[-1] == 0, z'[1] == 0}, {x, y, z}, t] // FullySimplify // First 

I get the following output

ReplaceAll::reps: {Dsolve[{x''[t] == -c3 - c2 z[t] - c1 y'[t], <<8>>}, {x, y, z}, t]} 

 is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. 

Set::shape: Lists {x, y, z} and {x, y, z} /. Dsolve[{x''[t] == 

-c3 - c2 z[t] - c1 y'[t], <<8>>}, {x, y, z}, t] are not the same shape. 

Could someone please tell me what is wrong with my approach and please suggest me how to solve this system.
Thank you for your time

I have three coupled second order ODE's given as below

$x''[t] = -c_1*y'[t]-c_2*z[t]-c_3$
$y''[t] = -c_4*x'[t]$
$z''[t] = \frac{c_5}{c_6}*x[t]-c_6$

where $c_i$'s are know constants. The boundary conditions are

$x[-1]=x[1]=y[-1]=y[1]=z'[-1]=z'[1]=0$.

I followed the example given here How do I solve coupled ordinary differential equations?

{x, y, z} = {x, y, z} /. Dsolve[{x''[t] == -c1*y'[t] - c2*z[t] - c3, y''[t] == -c4*x'[t], z''[t] == -c5 + c5*x[t]/c6, x[-1] == 0, x[1] == 0, y[-1] == 0, y[1] == 0, z'[-1] == 0, z'[1] == 0}, {x, y, z}, t] // FullySimplify // First 

I get the following output

ReplaceAll::reps: {Dsolve[{x''[t] == -c3 - c2 z[t] - c1 y'[t], <<8>>}, {x, y, z}, t]} 

 is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. 

Set::shape: Lists {x, y, z} and {x, y, z} /. Dsolve[{x''[t] == 

-c3 - c2 z[t] - c1 y'[t], <<8>>}, {x, y, z}, t] are not the same shape. 

Could someone please tell me what is wrong with my approach and please suggest me how to solve this system.
Thank you for your time

I have three coupled second order ODE's given as below

$x''[t] = -c_1*y'[t]-c_2*z[t]-c_3$
$y''[t] = -c_4*x'[t]$
$z''[t] = \frac{c_5}{c_6}*x[t]-c_6$

where $c_i$'s are know constants. The boundary conditions are

$x[-1]=x[1]=y[-1]=y[1]=z'[-1]=z'[1]=0$.

I followed the example given here How do I solve coupled ordinary differential equations?

In[1]:= {x, y, z} = {x, y, z} /. Dsolve[{x''[t] == -c1*y'[t] - c2*z[t] - c3, y''[t] == -c4*x'[t], z''[t] == -c5 + c5*x[t]/c6, x[-1] == 0, x[1] == 0, y[-1] == 0, y[1] == 0, z'[-1] == 0, z'[1] == 0}, {x, y, z}, t] // FullySimplify // First 

I get the following output

ReplaceAll::reps: {Dsolve[{x''[t] == -c3 - c2 z[t] - c1 y'[t], <<8>>}, {x, y, z}, t]} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing.

Set::shape: Lists {x, y, z} and {x, y, z} /.
Dsolve[{x''[t] == -c3 - c2 z[t] - c1 y'[t], <<8>>}, {x, y, z}, t] are not the same shape.

Could someone please tell me what is wrong with my approach and please suggest me how to solve this system.
Thank you for your time

I have three coupled second order ODE's given as below

$x''[t] = -c_1*y'[t]-c_2*z[t]-c_3$
$y''[t] = -c_4*x'[t]$
$z''[t] = \frac{c_5}{c_6}*x[t]-c_6$

where $c_i$'s are know constants. The boundary conditions are

$x[-1]=x[1]=y[-1]=y[1]=z'[-1]=z'[1]=0$.

I followed the example given here How do I solve coupled ordinary differential equations?

{x, y, z} = {x, y, z} /. Dsolve[{x''[t] == -c1*y'[t] - c2*z[t] - c3, y''[t] == -c4*x'[t], z''[t] == -c5 + c5*x[t]/c6, x[-1] == 0, x[1] == 0, y[-1] == 0, y[1] == 0, z'[-1] == 0, z'[1] == 0}, {x, y, z}, t] // FullySimplify // First 

I get the following output

ReplaceAll::reps: {Dsolve[{x''[t] == -c3 - c2 z[t] - c1 y'[t], <<8>>}, {x, y, z}, t]} 

 is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. 

Set::shape: Lists {x, y, z} and {x, y, z} /. Dsolve[{x''[t] == 

-c3 - c2 z[t] - c1 y'[t], <<8>>}, {x, y, z}, t] are not the same shape. 

Could someone please tell me what is wrong with my approach and please suggest me how to solve this system.
Thank you for your time