Mixing
Solve $(2xy+e^x) dx + (x^2 y -sin{y}) dy=0$
$begingroup$
Solve: $(2xy+e^x) dx + (x^2 y -sin{y}) dy=0$
Clearly, the differential equation is not exact. After applying various methods to no avail, (including power series and Fourier expansion) I cannot see how to get to the solution (an approximating polynomial will do). Online tools are useless here too. Maybe treating it analytically is the only way.
Or does it have a simple solution which I am missing?
real-analysis ordinary-differential-equations approximation
asked Jan 29 at 19:02
Subhasis BiswasSubhasis Biswas
512412
$endgroup$
add a comment |
$begingroup$
Solve: $(2xy+e^x) dx + (x^2 y -sin{y}) dy=0$
Clearly, the differential equation is not exact. After applying various methods to no avail, (including power series and Fourier expansion) I cannot see how to get to the solution (an approximating polynomial will do). Online tools are useless here too. Maybe treating it analytically is the only way.
Or does it have a simple solution which I am missing?
real-analysis ordinary-differential-equations approximation
asked Jan 29 at 19:02
Subhasis BiswasSubhasis Biswas
512412
$endgroup$
$begingroup$
I cannot see one. What could it be?
$endgroup$
– Subhasis Biswas
Jan 29 at 19:05
$begingroup$
Your equation has no solution in the known elementary functions
$endgroup$
– Dr. Sonnhard Graubner
Jan 29 at 19:07
$begingroup$
Then let us try to brute force it
$endgroup$
– Subhasis Biswas
Jan 29 at 19:10
add a comment |
$begingroup$
Solve: $(2xy+e^x) dx + (x^2 y -sin{y}) dy=0$
Clearly, the differential equation is not exact. After applying various methods to no avail, (including power series and Fourier expansion) I cannot see how to get to the solution (an approximating polynomial will do). Online tools are useless here too. Maybe treating it analytically is the only way.
Or does it have a simple solution which I am missing?
real-analysis ordinary-differential-equations approximation
asked Jan 29 at 19:02
Subhasis BiswasSubhasis Biswas
512412
$endgroup$
Solve: $(2xy+e^x) dx + (x^2 y -sin{y}) dy=0$
Clearly, the differential equation is not exact. After applying various methods to no avail, (including power series and Fourier expansion) I cannot see how to get to the solution (an approximating polynomial will do). Online tools are useless here too. Maybe treating it analytically is the only way.
Or does it have a simple solution which I am missing?
real-analysis ordinary-differential-equations approximation
real-analysis ordinary-differential-equations approximation
asked Jan 29 at 19:02
Subhasis BiswasSubhasis Biswas
512412
asked Jan 29 at 19:02
Subhasis BiswasSubhasis Biswas
512412
asked Jan 29 at 19:02
Subhasis BiswasSubhasis Biswas
512412
asked Jan 29 at 19:02
Subhasis BiswasSubhasis Biswas
512412
asked Jan 29 at 19:02
Subhasis BiswasSubhasis Biswas
512412
512412
$begingroup$
I cannot see one. What could it be?
$endgroup$
– Subhasis Biswas
Jan 29 at 19:05
$begingroup$
Your equation has no solution in the known elementary functions
$endgroup$
– Dr. Sonnhard Graubner
Jan 29 at 19:07
$begingroup$
Then let us try to brute force it
$endgroup$
– Subhasis Biswas
Jan 29 at 19:10
add a comment |
$begingroup$
I cannot see one. What could it be?
$endgroup$
– Subhasis Biswas
Jan 29 at 19:05
$begingroup$
Your equation has no solution in the known elementary functions
$endgroup$
– Dr. Sonnhard Graubner
Jan 29 at 19:07
$begingroup$
Then let us try to brute force it
$endgroup$
– Subhasis Biswas
Jan 29 at 19:10
$begingroup$
I cannot see one. What could it be?
$endgroup$
– Subhasis Biswas
Jan 29 at 19:05
$begingroup$
I cannot see one. What could it be?
$endgroup$
– Subhasis Biswas
Jan 29 at 19:05
$begingroup$
Your equation has no solution in the known elementary functions
$endgroup$
– Dr. Sonnhard Graubner
Jan 29 at 19:07
$begingroup$
Your equation has no solution in the known elementary functions
$endgroup$
– Dr. Sonnhard Graubner
Jan 29 at 19:07
$begingroup$
Then let us try to brute force it
$endgroup$
– Subhasis Biswas
Jan 29 at 19:10
$begingroup$
Then let us try to brute force it
$endgroup$
– Subhasis Biswas
Jan 29 at 19:10
add a comment |
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$begingroup$
I cannot see one. What could it be?
$endgroup$
– Subhasis Biswas
Jan 29 at 19:05
$begingroup$
Your equation has no solution in the known elementary functions
$endgroup$
– Dr. Sonnhard Graubner
Jan 29 at 19:07
$begingroup$
Then let us try to brute force it
$endgroup$
– Subhasis Biswas
Jan 29 at 19:10