Unable to find symbolic solution with "dsolve" function

I've used the dsolve() function before, but for some reason it isn't working well for me on this particular problem. The differential equation is dy/dt=(t-e^(-t))/(y+e^y), with an initial value of y(1.5)=0.5.

    sol=dsolve('Dy=(t-exp(-t))/(y+(exp(y)))','y(1.5)=0.5','t')

These are the warnings I get:

In dsolve (line 126)

Warning: Unable to find symbolic solution.

> In dsolve>assignOutputs (line 242)

In dsolve (line 228)

and "sol" gets [empty sym], when it should get me an equation.

[VBBV]

Define t as symbolic variable

syms y t
eqn = diff(y,t) == t-exp(-t)/(y+exp(y));
Cond = y(1.5)==0.5
S= dsolve(eqn,Cond);

[Walter Roberson]

unfortunately that does not solve the problem

[Lucas Howarth]

What do I do then??

[VBBV]

install symbolic math toolbox and run it

[Lucas Howarth]

Is there not another simpler way? This is only my class's 3rd MATLAB assignment, and I don't think we need to install additional things.

[Lucas Howarth]

I think it has to do with the "exp(y)" in the denominator. I can dsolve() the equation fine if I take that out. Maybe it has to do with the domain/range??

[VBBV]

or use ode45

syms y t
eqn = @(y,t) t-exp(-t)/(y+exp(y));
y0 = 0.5;
span = [0 1];
[t y] = ode45(eqn,span,y0)

[Lucas Howarth]

Yeah I actually use ode45 earlier in my code, but my teacher wants us to also plot the real solution that we get using dsolve().

[Walter Roberson]

dsolve() is the symbolic toolbox. If you are being asked to use dsolve() then you are being asked to use the symbolic toolbox.

[Bhomik Kankaria]

Hi Lucas,

If dsolve cannot find an explicit solution of a differential equation analytically, then it returns an empty symbolic array. You can solve the differential equation by using MATLAB® numerical solver, such as ode45. For more information, see Solve a Second-Order Differential Equation Numerically.

Alternatively, you can try finding an implicit solution of the differential equation by specifying the 'Implicit' option to true.For example, in your case you can use it to solve the equation -

>> dsolve('Dy=(t-exp(-t))/(y+(exp(y)))','y(1.5)=0.5','t','Implicit',true)

[Walter Roberson]

By the way, Maple is not able to solve the equation.