I get explicit solution not found , how to view the solution ?

syms x(t) y(t)

dx = diff(x,t)
dx2=diff(x,t,2)
dy = diff(y,t)
dy2=diff(y,t,2)

eqns = [dx2 + dx2 == y - 2*dx*dy + 2*(dx).^2+cos(t), dy2 == 2*y + x*dy];

conds = [y(0)==0, dy(0)==1, x(0)==0, dx(0)==0];

sol = dsolve(eqns,conds)

[Jan]

What is your question? Did you take into account, that this function might not have an explicit solution?

[madhan ravi]

[madhan ravi]

I have to reduce it into linear differential order equation and solve it. I get the same warning for (c),(d) & (e)

[Stephan]

Have a look at this:

https://de.mathworks.com/help/symbolic/reducedifferentialorder.html?s_tid=doc_ta

Does this help you?

Best regards

Stephan

[Star Strider]

Another option is the odeToVectorField (link) function.

[madhan ravi]

it could be better if someone could solve the problem because it's hard for me to understand.

[Stephan]

Sorry,

but this is not the homework service here...

Best regards

Stephan

[Walter Roberson]

You made a mistake in the equations. The second equation has y'' on the left hand side, but you used dx2 which is x'' .

[madhan ravi]

Thank you so much

[madhan ravi]

[Jan]

Please post the code as text. We cannot scroll to the right on your screenshot.

[madhan ravi]

Mr. Jan the code is in the first comment :)

Answer 1

[Walter Roberson]

If you temporarily leave out the conditions on the derivatives, then Maple says that the solution is

x(t) = -ln(-2*(-(1/2)*MathieuC(0, -1, (1/2)*t)-_C2*MathieuS(0, -1, (1/2)*t))/(MathieuSPrime(0, -1, (1/2)*t)*MathieuC(0, -1, (1/2)*t)-MathieuCPrime(0, -1, (1/2)*t)*MathieuS(0, -1, (1/2)*t)))-(2*I)*Pi*_Z1
y(t) = 0

where _Z1 is an arbitrary integer (that is, there is a family of solutions spaced 2*Pi*I apart) and _C2 is a constant of integration.

Now let us consider dy(0)==1 . But y(t) is the constant 0, so dy is the constant 0, so dy(0) can never be 1.

The system is potentially inconsistent. (I say "potentially" because Maple does not always find all of the potential solutions.)

The condition dx(0)=0 is fine: it can be resolved as _C2 = 0