Does anyone have any ideas on how to solve diff. equations like the one attached in matlab or mathcad? I know that I need to have initial boundary conditions in order to solve but I'm not sure about anything else?

2. I haven't looked at your specific equation, but have you tried $\displaystyle dsolve?$

DSOLVE Symbolic solution of ordinary differential equations.
DSOLVE('eqn1','eqn2', ...) accepts symbolic equations representing
ordinary differential equations and initial conditions. Several
equations or initial conditions may be grouped together, separated
by commas, in a single input argument.

By default, the independent variable is 't'. The independent variable
may be changed from 't' to some other symbolic variable by including
that variable as the last input argument.

The letter 'D' denotes differentiation with respect to the independent
variable, i.e. usually d/dt. A "D" followed by a digit denotes
repeated differentiation; e.g., D2 is d^2/dt^2. Any characters
immediately following these differentiation operators are taken to be
the dependent variables; e.g., D3y denotes the third derivative
of y(t). Note that the names of symbolic variables should not contain
the letter "D".