Wronskian is infinite
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Given a differential equation $$xy''+y'+xy=0$$. I have to find the number of linearly independent solutions about $x=0$. My attempt is to find the Wronskian at $x=0$ which is infinity. I cannot understand how to proceed.
differential-equations
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Given a differential equation $$xy''+y'+xy=0$$. I have to find the number of linearly independent solutions about $x=0$. My attempt is to find the Wronskian at $x=0$ which is infinity. I cannot understand how to proceed.
differential-equations
1
This is a well-studied DifEq and has solution $y(x) = c_1 J_0(x) + c_2 Y_0(x)$ in terms of Bessel Functions. You can show this, e.g., by supposing $y$ is analytic and working with the power series. Knowing this, you should get two linearly independent solutions.
â Brevan Ellefsen
Sep 9 at 10:40
1
Another thing to try (if you do not know about Bessel functions) is series solution of the DE.
â GEdgar
Sep 9 at 10:54
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Given a differential equation $$xy''+y'+xy=0$$. I have to find the number of linearly independent solutions about $x=0$. My attempt is to find the Wronskian at $x=0$ which is infinity. I cannot understand how to proceed.
differential-equations
Given a differential equation $$xy''+y'+xy=0$$. I have to find the number of linearly independent solutions about $x=0$. My attempt is to find the Wronskian at $x=0$ which is infinity. I cannot understand how to proceed.
differential-equations
differential-equations
asked Sep 9 at 10:29
Purushothaman
1976
1976
1
This is a well-studied DifEq and has solution $y(x) = c_1 J_0(x) + c_2 Y_0(x)$ in terms of Bessel Functions. You can show this, e.g., by supposing $y$ is analytic and working with the power series. Knowing this, you should get two linearly independent solutions.
â Brevan Ellefsen
Sep 9 at 10:40
1
Another thing to try (if you do not know about Bessel functions) is series solution of the DE.
â GEdgar
Sep 9 at 10:54
add a comment |Â
1
This is a well-studied DifEq and has solution $y(x) = c_1 J_0(x) + c_2 Y_0(x)$ in terms of Bessel Functions. You can show this, e.g., by supposing $y$ is analytic and working with the power series. Knowing this, you should get two linearly independent solutions.
â Brevan Ellefsen
Sep 9 at 10:40
1
Another thing to try (if you do not know about Bessel functions) is series solution of the DE.
â GEdgar
Sep 9 at 10:54
1
1
This is a well-studied DifEq and has solution $y(x) = c_1 J_0(x) + c_2 Y_0(x)$ in terms of Bessel Functions. You can show this, e.g., by supposing $y$ is analytic and working with the power series. Knowing this, you should get two linearly independent solutions.
â Brevan Ellefsen
Sep 9 at 10:40
This is a well-studied DifEq and has solution $y(x) = c_1 J_0(x) + c_2 Y_0(x)$ in terms of Bessel Functions. You can show this, e.g., by supposing $y$ is analytic and working with the power series. Knowing this, you should get two linearly independent solutions.
â Brevan Ellefsen
Sep 9 at 10:40
1
1
Another thing to try (if you do not know about Bessel functions) is series solution of the DE.
â GEdgar
Sep 9 at 10:54
Another thing to try (if you do not know about Bessel functions) is series solution of the DE.
â GEdgar
Sep 9 at 10:54
add a comment |Â
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This is a well-studied DifEq and has solution $y(x) = c_1 J_0(x) + c_2 Y_0(x)$ in terms of Bessel Functions. You can show this, e.g., by supposing $y$ is analytic and working with the power series. Knowing this, you should get two linearly independent solutions.
â Brevan Ellefsen
Sep 9 at 10:40
1
Another thing to try (if you do not know about Bessel functions) is series solution of the DE.
â GEdgar
Sep 9 at 10:54