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Magazine Problem 7
For each equation, list all the singular points in the finite plane. $$ \left(1+x^{2}\right) y^{\prime \prime}-2 x y^{\prime}+6 y=0 $$
Problem 7
Find the general solution valid near the origin. Always state the region of validity of the solution. $$ \left(1+x^{2}\right) y^{\prime \prime}+10 x y^{\prime}+20 y=0 $$
Problem 8
For each equation, list all the singular points in the finite plane. $$ \left(x^{2}-4 x+3\right) y^{\prime \prime}+x^{2} y^{\prime}-4 y=0 $$.
Problem 8
Find the general solution valid near the origin. Always state the region of validity of the solution. $$ \left(x^{2}+4\right) y^{\prime \prime}+2 x y^{\prime}-12 y=0 $$
Problem 9
Find the general solution valid near the origin. Always state the region of validity of the solution. $$ \left(x^{2}-9\right) y^{\prime \prime}+3 x y^{\prime}-3 y=0 $$
Problem 9
For each equation, list all the singular points in the finite plane. $$ x^{2}(1-x)^{3} y^{\prime \prime}+(1+2 x) y=0 $$.
Problem 10
For each equation, list all the singular points in the finite plane. $$ 6 x y^{\prime \prime}+\left(1-x^{2}\right) y^{\prime}+2 y=0 $$.
Problem 10
Find the general solution valid near the origin. Always state the region of validity of the solution. $$ y^{\prime \prime}+2 x y^{\prime}+5 y=0 $$
Problem 11
For each equation, list all the singular points in the finite plane. $$ 4 x y^{\prime \prime}+y=0 $$.
Problem 11
Find the general solution valid near the origin. Always state the region of validity of the solution. $$ \left(x^{2}+4\right) y^{\prime \prime}+6 x y^{\prime}+4 y=0 $$
