please give me answer what is wrong

[현국 조]

Answer 1

[Star Strider]

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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[현국 조]

really thanks

[Star Strider]

As always, my pleasure!

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