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Magazine Problem 63
Solve the following equations using the method of undetermined coefficients. $$ y^{\prime \prime}+y=3 \sin 2 x+x \cos 2 x $$
Problem 64
Solve the following equations using the method of undetermined coefficients. $$ y^{\prime \prime}+3 y^{\prime}-28 y=10 e^{4 x} $$
Problem 65
Solve the following equations using the method of undetermined coefficients. $$ y^{\prime \prime}+10 y^{\prime}+25 y=x e^{-5 x}+4 $$
Problem 66
a. Write the form for the particular solution \(y_{p}(x)\) for the method of undetermined coefficients. b. Use a computer algebra system to find a particular solution to the given equation. $$ y^{\prime \prime}-y^{\prime}-y=x+e^{-x} $$
Problem 67
a. Write the form for the particular solution \(y_{p}(x)\) for the method of undetermined coefficients. b. Use a computer algebra system to find a particular solution to the given equation. $$ y^{\prime \prime}-3 y=x^{2}-4 x+11 $$
Problem 68
a. Write the form for the particular solution \(y_{p}(x)\) for the method of undetermined coefficients. b. Use a computer algebra system to find a particular solution to the given equation. $$ y^{\prime \prime}-y^{\prime}-4 y=e^{x} \cos 3 x $$
Problem 69
a. Write the form for the particular solution \(y_{p}(x)\) for the method of undetermined coefficients. b. Use a computer algebra system to find a particular solution to the given equation. $$ 2 y^{\prime \prime}-y^{\prime}+y=\left(x^{2}-5 x\right) e^{-x} $$
Problem 70
a. Write the form for the particular solution \(y_{p}(x)\) for the method of undetermined coefficients. b. Use a computer algebra system to find a particular solution to the given equation. $$ 4 y^{\prime \prime}+5 y^{\prime}-2 y=e^{2 x}+x \sin x $$
Problem 71
a. Write the form for the particular solution \(y_{p}(x)\) for the method of undetermined coefficients. b. Use a computer algebra system to find a particular solution to the given equation. $$ y^{\prime \prime}-y^{\prime}-2 y=x^{2} e^{x} \sin x $$
Problem 72
a. Write the form for the particular solution \(y_{p}(x)\) for the method of undetermined coefficients. b. Use a computer algebra system to find a particular solution to the given equation. $$ y^{\prime \prime}+3 y^{\prime}-4 y=2 e^{x} $$
