Euler Equations having double roots solutions
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If the Euler equation have the double roots as a solution, second solution will be $y_2(x)=x^rln{x}$. What is its proof? or how it can be derived? To find a second solution,we will use the fact that constant times the solution is also a solution to linear homogeneous differential equations. Now why do we choose $ln{x}$ as constant?why not any other constant?
ordinary-differential-equations self-learning
asked Dec 19 '18 at 6:56
Dhamnekar WinodDhamnekar Winod
427514
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add a comment |
$begingroup$
If the Euler equation have the double roots as a solution, second solution will be $y_2(x)=x^rln{x}$. What is its proof? or how it can be derived? To find a second solution,we will use the fact that constant times the solution is also a solution to linear homogeneous differential equations. Now why do we choose $ln{x}$ as constant?why not any other constant?
ordinary-differential-equations self-learning
asked Dec 19 '18 at 6:56
Dhamnekar WinodDhamnekar Winod
427514
$endgroup$
add a comment |
$begingroup$
If the Euler equation have the double roots as a solution, second solution will be $y_2(x)=x^rln{x}$. What is its proof? or how it can be derived? To find a second solution,we will use the fact that constant times the solution is also a solution to linear homogeneous differential equations. Now why do we choose $ln{x}$ as constant?why not any other constant?
ordinary-differential-equations self-learning
asked Dec 19 '18 at 6:56
Dhamnekar WinodDhamnekar Winod
427514
$endgroup$
If the Euler equation have the double roots as a solution, second solution will be $y_2(x)=x^rln{x}$. What is its proof? or how it can be derived? To find a second solution,we will use the fact that constant times the solution is also a solution to linear homogeneous differential equations. Now why do we choose $ln{x}$ as constant?why not any other constant?
ordinary-differential-equations self-learning
ordinary-differential-equations self-learning
asked Dec 19 '18 at 6:56
Dhamnekar WinodDhamnekar Winod
427514
asked Dec 19 '18 at 6:56
Dhamnekar WinodDhamnekar Winod
427514
edited Dec 19 '18 at 8:46
Dhamnekar Winod
asked Dec 19 '18 at 6:56
Dhamnekar WinodDhamnekar Winod
427514
asked Dec 19 '18 at 6:56
Dhamnekar WinodDhamnekar Winod
427514
asked Dec 19 '18 at 6:56
Dhamnekar WinodDhamnekar Winod
427514
427514
add a comment |
add a comment |
1 Answer
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One can find answer to this question here$rightarrow$[Euler equation having double roots or repeated roots as a solution1DE]
answered Dec 20 '18 at 7:19
Dhamnekar WinodDhamnekar Winod
427514
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add a comment |
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1 Answer
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1 Answer
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$begingroup$
One can find answer to this question here$rightarrow$[Euler equation having double roots or repeated roots as a solution1DE]
answered Dec 20 '18 at 7:19
Dhamnekar WinodDhamnekar Winod
427514
$endgroup$
add a comment |
$begingroup$
One can find answer to this question here$rightarrow$[Euler equation having double roots or repeated roots as a solution1DE]
answered Dec 20 '18 at 7:19
Dhamnekar WinodDhamnekar Winod
427514
$endgroup$
add a comment |
$begingroup$
One can find answer to this question here$rightarrow$[Euler equation having double roots or repeated roots as a solution1DE]
answered Dec 20 '18 at 7:19
Dhamnekar WinodDhamnekar Winod
427514
$endgroup$
One can find answer to this question here$rightarrow$[Euler equation having double roots or repeated roots as a solution1DE]
answered Dec 20 '18 at 7:19
Dhamnekar WinodDhamnekar Winod
427514
edited Dec 21 '18 at 5:20
answered Dec 20 '18 at 7:19
Dhamnekar WinodDhamnekar Winod
427514
answered Dec 20 '18 at 7:19
Dhamnekar WinodDhamnekar Winod
427514
answered Dec 20 '18 at 7:19
Dhamnekar WinodDhamnekar Winod
427514
427514
add a comment |
add a comment |
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