Programming error with a model function

I don't understand why but I'm getting an error message regarding my Matlab script:

I'm trying to code for the example equation

y′1=y′2

y2=A/Bty1.

tspan = [0 5];
y0 = [0 0.1];
A = 1;
B = 2;
[t,yAB] = ode15s(@fun40,tspan,y0);

Unrecognized function or variable 'dyB'.

Error in solution>fun40 (line 11)
dyA(1) = dyB(2);

Error in odearguments (line 92)
f0 = ode(t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode15s (line 153)
odearguments(odeIsFuncHandle, odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);

figure
semilog(t,y)
grid
function dyAB = fun40(t,yAB)
dyAB = zeros(2,1);
dyA(1) = dyB(2);
dyB(2) = (A/B)*t.*dyA(1);
end

Answer 1

[Torsten]

If your system of differential equations really reads

y1' = y2'
y2 = A/B * t * y1

it follows

y2' = A/B * y1 + A/B * t * y1' 

thus

y1' = A/B * y1 / (1- A/B * t)

syms t y1(t)
syms A B real 
eqn = diff(y1,t) == A/B * y1 / (1- A/B * t)

eqn(t) = 

y1sol = dsolve(eqn)

y1sol = 

y2sol = A/B * t * y1sol

y2sol = 

diff(y1sol,t)

ans = 

simplify(diff(y2sol,t))

ans = 

Answer 2

[Walter Roberson]

tspan = [0 5];
y0 = [0 0.1];
A = 1;
B = 2;
[t,yAB] = ode15s(@(t,y)fun40(t,y,A,B),tspan,y0);
figure
plot(t,yAB)
grid
ylim([-0.01 0.11])

function dyAB = fun40(t,yAB,A,B)
    dyAB = zeros(2,1);
    dyA(1) = yAB(2);
    dyB(2) = (A/B)*t.*yAB(1);
end

[Walter Roberson]

syms A B positive
syms y1(t) y2(t)
dy1 = diff(y1);
dy2 = diff(y2);
eqn1 = dy1 == dy2

eqn1(t) = 

eqn2 = y2 == A/B * t * y1

eqn2(t) = 

sol = dsolve([eqn1, eqn2])

Warning: Unable to find symbolic solution.

 
sol =
 
[ empty sym ]
 

However, if the derivatives of the two functions are equal then the two functions differ only by a constant, and so you can substitute into

syms C
y1 = y2 + C

y1(t) = 

eqn3 = y2 == A/B * t * y1

eqn3(t) = 

sol = isolate(eqn3, y2)

sol = 

y2 = rhs(sol)

y2 = 

y1 = simplify(y2 + C)

y1 = 

simplify(diff(y1) - diff(y2))

ans = 

0