Solving 4th degree differential equations

[DP_10733008]

Good evening,

I am trying to solve an exercise in MathCad prime 8.0 with the RKadapt function but it return a very unusual error that says "Unknown error: Exception generated by call destination", I have tried to change the function with "Adams" or "rkfixed" and it returns the same error, I have also tried to redefine the equivalences as for example "(d/dr)^2 y(r)1 = y3". Attached there is a screeshot of my work sheet with the differential equation that I need to solve and the procedure that I did.

Thanks to everyone in advance.

[Werner_E]

Please attach your worksheet!

Just a stab in the blue ... try changing the second argument 0 to something positive, like 0.0001.

r=0 yields of course a division by zero! Maybe the reason for the unusual and less helpful error message you get.

[DP_10733008]

I have tried your suggestion but it doesn't work. I have attached the entire worksheet but it is written in italian, If you need any clarification just ask me.

Thanks.

[LucMeekes]

What is (capital) R defined to be?

Success!

Luc

[DP_10733008]

R is the radius of the disk in the figure in page 14, I have used it in the function because I need to calculate the displacement of the disk in the z direction, which is the solution of the equation from the center of the disk to the end of it.

Thanks again,

[Werner_E · Accepted solution]

You forgot to define B (in front of the definition of D_) - Probbably it should be B_plate

This seems to be the reason for the error along with the zero argument I already mentioned.

[DP_10733008]

Thank you a lot for your help, I have now realized the mistake. Now it shows the graphs as you have shown in the previous answer.

Thanks again.

[LucMeekes]

A couple of funny thing are going on here.

1. If I change Rkadapt to rkfixed I get an error message about incompatible units. This can be corrected by changing the second argument to to 0.001 m.

2. The value of w at R is calculated to be:

then why does the graph for S<1> versus S<0> show the value at 0.4 m to be near -6*10^-6 ?

Using the (my) symbolic solution, the graph is:

Success!
Luc

[LucMeekes]

Some hand calculation suggests that 

w(r)=(-q/B)*r^4/64

Success!

Luc

[DP_10733008]

Thanks for your help, but I need to obtain the solution using the mathcad solver for this exercise.