please give me answer what is wrong

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Accepted Answer

Star Strider
Star Strider on 21 Oct 2021
The differential equaton apparently does not have an analytic solution.
Integrating it numerically is an option —
syms y(x) x Y
Dy = diff(y);
eqn = (x*exp(x)+y+exp(y)+3)*diff(x) + (x*exp(y)+x+2)*Dy == 0;
isoeqn = isolate(eqn,Dy)
isoeqn = 
cond = y(0) == 0;
ySolx = dsolve(eqn,cond)
Warning: Unable to find symbolic solution.
ySolx = [ empty sym ]
[VF,Subs] = odeToVectorField(eqn)
VF = 
Subs = 
eqnfcn = matlabFunction(VF, 'Vars',{x,Y})
eqnfcn = function_handle with value:
@(x,Y)[-(exp(Y(1))+x.*exp(x)+Y(1)+3.0)./(x+x.*exp(Y(1))+2.0)]
tspan = [0 2.5];
ic = 0;
[x,y] = ode45(eqnfcn, tspan, ic);
figure
plot(x, y)
grid
xlabel('x')
ylabel('y')
legend(string(Subs), 'Location','best')
Experiment to get different results.
.

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