Matlab-解微分方程

Question

i'm trying to solve this equation:

y''+3yy'' with y(0)=0 ; y(2)=1

I've tried using bvp4c and i know i have to turn it into a system of DE but i am really stuck, any help would be appreciated, thanks :)

I've tried this, but really is just guessing

function sss=sos()
solinit=bvpinit(linspace(0,2,10),[1,0,0]);
answ=bvp4c(@twoode,@bcfun,solinit)
x=linspace(0,2);
y=deval(answ,x);
plot(x,y(1,:));
end

function dydx=twoode(x,y)
dydx=[y(3),3*y(1)+y(2)];
end

function res=bcfun(ya,yb)
res=[ya(1),yb(1)+2];
end

Answer 1

Start with (if the original equation is y'' + 3 * y * y' = 0)

function sss = sos()
solinit = bvpinit(linspace(0, 2, 10), [1, 0]);
answ = bvp4c(@twoode, @bcfun, solinit);
x = linspace(0, 2);
y = deval(answ, x);
plot(x, y(1, :));
end

function dydx = twoode(x, y)
dydx = [y(2); -3 * y(1) * y(2)];
end

function res = bcfun(ya, yb)
res = [ya(1); yb(1) - 1];
end