Why is ySol(t) = Dsolve(ode,cond) wrong? What should it be instead?

I solved the ODE by subsituting the the data in 'C' (numerous values) and i got a series of around 10 ODE eqs that look like this (heres one as an example):

ode(t) = diff(y(t), t)= 83136/832 - (100*y(t))/5

I want to solve for y(t) for all 10 eqs so i tried

ySol(t) = dsolve(ode,cond)

with the cond being

cond = y(0) == C

where C is workspace of 10 know values which i used to solve for the ode

this is the wrong part which i cant right

ySol(t) = dsolve(ode,cond)

any ideas on how i can solve the 10 odes for y(t)??

Warning: Number of equations greater than number of indeterminates. Trying heuristics to reduce

to square system.

> In symengine

In mupadengine/evalin_internal

In mupadengine/feval_internal

In dsolve>mupadDsolve (line 334)

In dsolve (line 203)

Error using mupadengine/feval_internal

Unable to reduce to square system because the number of equations differs from the number of

indeterminates.

Error in dsolve>mupadDsolve (line 334)

T = feval_internal(symengine,'symobj::dsolve',sys,x,options);

Error in dsolve (line 203)

sol = mupadDsolve(args, options);

Answer 1

[Torsten]

syms Cs t y(t)
ode = diff(y,t) == 40*Cs-40/280*y;
cond = y(0) == Cs;
ySol(t) = dsolve(ode,cond);
ysol_num = subst(ySol,Cs,C)

[Yasmine Abdu]

(just edited the question for clarity)I solved the ODE by subsituting the the data in 'C' (numerous values) and i got a series of around 10 ODE eqs that look like this (heres one as an example):

ode(t) = diff(y(t), t)= 83136/832 - (100*y(t))/5

I want to solve for y(t) for all 10 eqs so i tried

ySol(t) = dsolve(ode,cond)

with the cond being

cond = y(0) == C

where C is workspace of 10 know values which i used to solve for the ode

this is the wrong part which i cant right

ySol(t) = dsolve(ode,cond)

any ideas on how i can solve the 10 odes for y(t)??

[Torsten]

We understood this.

You will first have to solve one ODE with a symbolic variable for C (here Cs).

Then you can substitute your 10 values for C into the solution to obtain 10 solutions.

[Yasmine Abdu]

Ahhhh right. Thank you very much for explaining this!

Answer 2

[Paul]

I think the ode needs to be solved first, and then sub in the values of y(0) to get the family of solutions (if I understand the question)

syms y(t) C
ode = diff(y,t) == 40*C-40/280*y;
ysol(t) = dsolve(ode)

ysol(t) = 

Now solve for the constant C1 by enforcing the initial condition

syms C1
C1 = solve(ysol(0) == C,C1)

C1 = 

Now sub back into the solution

ysol(t) = subs(ysol(t))

ysol(t) = 

Now sub in some values of C for specific initial conditions

y(t) = subs(ysol(t),C,[1 2])

y(t) = 

[Yasmine Abdu]

(just edited the question for clarity)I solved the ODE by subsituting the the data in 'C' (numerous values) and i got a series of around 10 ODE eqs that look like this (heres one as an example):

ode(t) = diff(y(t), t)= 83136/832 - (100*y(t))/5

I want to solve for y(t) for all 10 eqs so i tried

ySol(t) = dsolve(ode,cond)

with the cond being

cond = y(0) == C

where C is workspace of 10 know values which i used to solve for the ode

this is the wrong part which i cant right

ySol(t) = dsolve(ode,cond)

any ideas on how i can solve the 10 odes for y(t)??

[Paul]

As far as I know, if you want to solve 10 odes using one call to dsolve, you'll need to have 10 functions to solve for, like y1(t), y2(t), etc.

Or, you can solve the equation once with C as a parameter, and then sub in the 10 values of C to get the 10 solutions, as both I and @Torsten, have shown. Is there a reason this approach is not acceptable?

I suppose another option is to define the 10 odes a priori and then loop through dsolve to solve each, like this:

C = [1 2];
syms y(t)
odes = diff(y(t),t) == 40*C-40/280*y;
odes = odes(t);
for ii = 1:numel(C)
ysol(ii) = dsolve(odes(ii),y(0)==C(ii));
end
ysol

ysol = 

which yields the same result shown above.

[Yasmine Abdu]

Thank you for the great explainations- i see where ive been going wrong it makes perfect sense now.