How to add "erf()" part to the ode solution?

Hi,

I have the ODE : y' = -x+2+10*e^(10*(x-1)^2)

I have numeric solution of below:

I have a analytical solution of ODE below:

y (x)= C1 + 2*x - x^2/2 + (10^(1/2)*pi^(1/2)*erfi(10^(1/2)*(x - 1)))/2, y(0)=1

when I plot the analytical solution without "erfi()" part, the graph is below:

The curve is similar to numarical solution but there is evident error. I think, this error is because of "erf" part of the analytical solution. How can I plot the analytical solution with the "erf()" part. Thank you.

Answer 1

[Torsten]

syms x y(x)
eqn = diff(y,x) - (-x+2+10*exp(-10*(x-1)^2)) == 0;
cond = y(0)==1;
sol = dsolve(eqn,cond)

sol = 

fplot(sol,[0 6])

[Ali Deniz]

Thank you very much.

[Les Beckham]

Without the symbolic toolbox:

x = linspace(0, 6, 1000);
rt = sqrt(10);
rp = sqrt(pi);
y = 2*x - x.^2/2 + (rt*rp*erf(rt))/2 + (rt*rp*erf(rt*(x-1)))/2 + 1;
plot(x,y)
grid on

[Ali Deniz]

Thank you very much.

-Ali