how to solve differential equation sympolically

It depends on a given DGL.

Please post it, then we can tell you if it is solvable symbolically or not.

best regards, Volker

Only numerical in Mathcad.

But you can solve any simple DE thru using symbolical operator of Mathcad.

Or use

Wolfram|Alpha: Computational Knowledge Engine

Yes, we can.

See here A classical math problem: differential equations.

Note that it applies to Mathcad version 11. Though the method is universally applicable, for nth order DE's, automaticity as shown here is only obtained via Mathcad 11.

Mathcad 12 and up, as well as any version of Prime require more hand-work.

Luc

As you could hear - Mathcad does not provide a way to solve ODEs symbolically out-of-the-box as other math software.

But you can use Mathcad's limited symbolic capabilities to find a symbolic solution to a given ODE.

Lucs approach using laplace transforms worked super fine and automatically in Mathcad 11, but the same method requires more manual work in Mathcad 14/15.

I once played around in MC14 to atomatically solve ODE's and only fnished a small routine for simple first order ODEs (posted it here: Re: Direction Field Plots (ODE's)‌‌. I guess that at least some parts of that sheet won't work in Prime.

So you see - the newer the version, the less the features 😞

Analytical solution of a Type IV differential equation of higher order: