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Problem 11

For each equation, list all of the singular points in the finite plane. \(4 x y^{\prime \prime}+y=0\)

Problem 12

For each equation, list all of the singular points in the finite plane. \(4 y^{\prime \prime}+y=0\)

Problem 12

Unless it is otherwise requested, find the general solution valid near the origin. Always state the region of validity of the solution. \(\left(1+2 x^{2}\right) y^{\prime \prime}-5 x y^{\prime}+3 y=0\)

Problem 13

For each equation, list all of the singular points in the finite plane. \(x^{2}\left(x^{2}-9\right) y^{\prime \prime}+3 x y^{\prime}-y=0\)

Problem 13

Unless it is otherwise requested, find the general solution valid near the origin. Always state the region of validity of the solution. \(y^{\prime \prime}+x^{2} y=0\)

Problem 14

Unless it is otherwise requested, find the general solution valid near the origin. Always state the region of validity of the solution. \(y^{\prime \prime}-2(x+3) y^{\prime}-3 y=0 .\) Solve about \(x=-3\)

Problem 14

For each equation, list all of the singular points in the finite plane.\(x^{2}\left(1+4 x^{2}\right) y^{\prime \prime}-4 x y^{\prime}+y=0\)

Problem 15

For each equation, list all of the singular points in the finite plane. \((2 x+1)(x-3) y^{\prime \prime}-y^{\prime}+(2 x+1) y=0\)

Problem 16

For each equation, list all of the singular points in the finite plane. \(x^{3}\left(x^{2}-4\right)^{2} y^{\prime \prime}+2\left(x^{2}-4\right) y^{\prime}-x y=0\)

Problem 16

Unless it is otherwise requested, find the general solution valid near the origin. Always state the region of validity of the solution. \(\left(1-4 x^{2}\right) y^{\prime \prime}+6 x y^{\prime}-4 y=0\)

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