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.










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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.
    – 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.
    – GEdgar
    Sep 9 at 10:54















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.










share|cite|improve this question

















  • 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.
    – 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.
    – GEdgar
    Sep 9 at 10:54













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.










share|cite|improve this question













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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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.
    – 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.
    – GEdgar
    Sep 9 at 10:54













  • 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.
    – 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.
    – 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.
– 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.
– 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.
– GEdgar
Sep 9 at 10:54





Another thing to try (if you do not know about Bessel functions) is series solution of the DE.
– GEdgar
Sep 9 at 10:54
















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