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Magazine Problem 5
Find power series solutions in powers of \(x\) of each of the differential equations in Exercises. $$ y^{\prime \prime}+x y^{\prime}+\left(2 x^{2}+1\right) y=0 $$
Problem 5
Use the method of Frobenius to find solutions near \(x=0\) of each of the differential equations in Exercises, $$ 2 x^{2} y^{\prime \prime}+x y^{\prime}+\left(x^{2}-1\right) y=0 $$
Problem 6
Find power series solutions in powers of \(x\) of each of the differential equations in Exercises. $$ y^{\prime \prime}+x y^{\prime}+\left(x^{2}-4\right) y=0 $$
Problem 7
Find power series solutions in powers of \(x\) of each of the differential equations in Exercises. $$ y^{\prime \prime}+x y^{\prime}+(3 x+2) y=0 $$
Problem 8
Find power series solutions in powers of \(x\) of each of the differential equations in Exercises. $$ y^{\prime \prime}-x y^{\prime}+(3 x-2) y=0 $$
Problem 8
Use the method of Frobenius to find solutions near \(x=0\) of each of the differential equations in Exercises, $$ x^{2} y^{\prime \prime}-x y^{\prime}+\left(2 x^{2}+\frac{5}{9}\right) y=0 $$
Problem 9
Find power series solutions in powers of \(x\) of each of the differential equations in Exercises. $$ y^{\prime \prime}-\left(x^{3}+2\right) y^{\prime}-6 x^{2} y=0 $$
Problem 9
Use the method of Frobenius to find solutions near \(x=0\) of each of the differential equations in Exercises, $$ x^{2} y^{\prime \prime}+x y^{\prime}+\left(x^{2}-\frac{1}{9}\right) y=0 $$
Problem 10
Find power series solutions in powers of \(x\) of each of the differential equations in Exercises. $$ \left(x^{2}+1\right) y^{\prime \prime}+x y^{\prime}+x y=0 $$
Problem 11
Find power series solutions in powers of \(x\) of each of the differential equations in Exercises. $$ \left(x^{2}+1\right) y^{\prime \prime}+x y^{\prime}+x y=0 $$
