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Magazine Problem 6
Solve the differential equation or initial-value problem using the method of undetermined coefficients. $$ y^{\prime \prime}-4 y^{\prime}+4 y=x-\sin x $$
Problem 7
Solve the differential equation. $$ 3 y^{\prime \prime}=4 y^{\prime} $$
Problem 7
Solve the differential equation or initial-value problem using the method of undetermined coefficients. $$ y^{\prime \prime}-2 y^{\prime}+5 y=\sin x, \quad y(0)=1, \quad y^{\prime}(0)=1 $$
Problem 8
Solve the differential equation or initial-value problem using the method of undetermined coefficients. $$ y^{\prime \prime}-y=x e^{2 x}, \quad y(0)=0, \quad y^{\prime}(0)=1 $$
Problem 8
Use power series to solve the differential equation. $$ y^{\prime \prime}=x y $$
Problem 8
Solve the differential equation. $$ y=y^{\prime \prime} $$
Problem 8
A spring has a mass of \(1 \mathrm{kg}\) and its damping constant is \(c=10 .\) The spring starts from its equilibrium position with a velocity of \(1 \mathrm{m} / \mathrm{s}\). Graph the position function for the following values of the spring constant \(k: 10,20,25,30,40\). What type of damping occurs in each case?
Problem 9
Solve the differential equation. $$ y^{\prime \prime}-4 y^{\prime}+13 y=0 $$
Problem 9
Use power series to solve the differential equation. $$ y^{\prime \prime}-x y^{\prime}-y=0, \quad y(0)=1, \quad y^{\prime}(0)=0 $$
Problem 9
Solve the differential equation or initial-value problem using the method of undetermined coefficients. $$ y^{\prime \prime}-y^{\prime}=x e^{x}, \quad y(0)=2, \quad y^{\prime}(0)=1 $$
