MATLAB: How to solve Leibnitz equation

analyticaldiff()integrationintegro-differentialleibnitznumerical

This equation is one dimensionel leibnitz equation. How can i solve this problem. I tried int(exp(-x^2),x) but it is wrong way. Can you help me?

Try this:

syms C t F(t) 
F(t) = sqrt(pi)/sym(2) * diff(erf(C*t),t)
F = vpa(F,2)

producing:

F(t) =
1.0*C*exp(-1.0*C^2*t^2)

YOu can write first,second and third derivative like below:

df = diff(f,t) ;   %f'
d2f = diff(f,t,t) ; % f''
d3f = diff(f,t,t,t) ; % f'''

Check below option also:

syms f(t)  
df = diff(f,t) ;
d2f = diff(df,t) ;
d3f = diff(d2f,t) ;
ode = d3f+df*d2f == 0
dsolve(ode)

syms f(t)  
df = diff(f,t) ;
d2f = diff(df,t) ;
d3f = diff(d2f,t) ;
ode = d3f+df*d2f == 0 ;
cond = d2f(sym('inf')) == -1 ;
dsolve(ode,cond)