Why is my code unable to find a symbolic solution?

Hello,

I am trying to find the solution to

t^2/(1+y^2),

and tried the following code, can someone help me fix this?

 syms y(t)
ode = diff(y,t) == t^2/(1+y^2);
ySol(t) = dsolve(ode)

Warning: Unable to find symbolic solution.

 
ySol(t) =
 
[ empty sym ]
 

Answer 1

[Dyuman Joshi]

dsolve() by default tries to find find an explicit solution analytically i.e. y in terms of t.

In this case, it is unable to find that form and thus returns the warning and an empty symbolic array.

However, you can get the implicit form of the solution -

syms y(t)
ode = diff(y,t) == t^2/(1+y^2);
ySol = dsolve(ode,'Implicit', true)

ySol = 

[Nina]

Ok, thank you!