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Magazine Problem 11
Find the general solution of each of the differential equations in exercise. $$ \frac{d^{2} y}{d x^{2}}+9 y=0 $$
Problem 12
Find the general solution of each of the differential equations in exercise. $$ 4 \frac{d^{2} y}{d x^{2}}+y=0 $$
Problem 12
Given that \(e^{-x}, e^{3 x}\), and \(e^{4 x}\) are all solutions of
$$
\frac{d^{3} y}{d x^{3}}-6 \frac{d^{2} y}{d x^{2}}+5 \frac{d y}{d x}+12 y=0
$$
show that they are linearly independent on the interval \(-\infty
Problem 13
Find the general solution of each of the differential equations in exercise. $$ \frac{d^{3} y}{d x^{3}}-5 \frac{d^{2} y}{d x^{2}}+7 \frac{d y}{d x}-3 y=0. $$
Problem 13
Given that \(x, x^{2}\), and \(x^{4}\) are all solutions of
$$
x^{3} \frac{d^{3} y}{d x^{3}}-4 x^{2} \frac{d^{2} y}{d x^{2}}+8 x \frac{d y}{d
x}-8 y=0
$$
show that they are linearly independent on the interval \(0
Problem 14
Find the general solution of each of the differential equations in exercise. $$ 4 \frac{d^{3} y}{d x^{3}}+4 \frac{d^{2} y}{d x^{2}}-7 \frac{d y}{d x}+2 y=0. $$
Problem 15
Find the general solution of each of the differential equations in exercise. $$ \frac{d^{3} y}{d x^{3}}-6 \frac{d^{2} y}{d x^{2}}+12 \frac{d y}{d x}-8 y=0. $$
Problem 16
Find the general solution of each of the differential equations in exercise. $$ \frac{d^{3} y}{d x^{3}}+4 \frac{d^{2} y}{d x^{2}}+5 \frac{d y}{d x}+6 y=0. $$
Problem 17
Find the general solution of each of the differential equations in exercise. $$ \frac{d^{3} y}{d x^{3}}-\frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}-y=0 $$
Problem 18
Find the general solution of each of the differential equations in exercise. $$ \frac{d^{4} y}{d x^{4}}+8 \frac{d^{2} y}{d x^{2}}+16 y=0. $$
