Unable to find symbolic solution with "dsolve" function

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Lucas Howarth 2020-10-9

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评论： Walter Roberson 2020-10-13

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.

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Bhomik Kankaria 2020-10-13

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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)