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Solving the ODE using DSolve returns the same input?

Posted 3 years ago

It directly returned this equation.

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POSTED BY: SHAOXUAN HUANG
2 Replies

Many ODEs do not have symbolic solutions in terms of commonly defined functions. The ODE in the question probably falls in that category. However, it should be noted that DSolve sometimes is unable to solve ODEs that do have symbolic solutions in terms of commonly defined functions.

Numerically:

sol = NDSolve[{-2 x - y[x]  == y'[x] (2 x^3 + 3 x^2 + x) + 
 Sqrt[x^2 (y[x]^2 - 4 y[x] + 7) + x (2 y[x]^2 - 7 y[x] + 9) + 
   y[x]^2 - 3 y[x] + 3], y[1] == 1}, y, {x, 1, 10}]
Plot[{y[x] /. sol, y'[x] /. sol}, {x, 1, 10}]

Regards M.I.

POSTED BY: Mariusz Iwaniuk
Posted 3 years ago

Thanks! But I am not sure if this one has a symbolic solution or not.

POSTED BY: SHAOXUAN HUANG
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