Chapter 31

Second-Order DE, Roots of Auxiliary Equation Not Real $$y^{\prime \prime}+4 y=0$$

Find the particular solution to each differential equation, using the given boundary conditions. \(y^{\prime \prime}-4 y^{\prime}=8, \quad y=y^{\prime}=0\) when \(x=0\)

Second-Order DE, Roots of Auxiliary Equation Not Real $$y^{\prime \prime}+2 y=0$$

Find the particular solution to each differential equation, using the given boundary conditions. \(y^{\prime \prime}+2 y^{\prime}-3 y=6, \quad y=0\) and \(y^{\prime}=2\) when \(x=0\)

Second-Order DE, Roots of Auxiliary Equation Not Real $$y^{\prime \prime}-4 y^{\prime}+5 y=0$$

Second-Order DE, Roots of Auxiliary Equation Not Real $$y^{\prime \prime}+10 y^{\prime}+425 y=0$$

Solve each differential equation. Use the given boundary conditions to find the constants of integration. $$y^{\prime \prime}+6 y^{\prime}+9 y=0, \quad y=0 \text { and } y^{\prime}=3 \text { when } x=0$$

Solve each differential equation. Use the given boundary conditions to find the constants of integration. $$y^{\prime \prime}+3 y^{\prime}+2 y=0, \quad y=0 \text { and } y^{\prime}=1 \text { when } x=0$$

Find the particular solution to each differential equation, using the given boundary conditions. \(y^{\prime \prime}-9 y=18 \cos 3 x+9, \quad y=-1\) and \(y^{\prime}=3\) when \(x=0\)

Solve each differential equation. Use the given boundary conditions to find the constants of integration. $$y^{\prime \prime}-2 y^{\prime}+y=0, \quad y=5 \text { and } y^{\prime}=-9 \text { when } x=0$$

Solve each differential equation. Use the given boundary conditions to find the constants of integration. $$y^{\prime \prime}+3 y^{\prime}-4 y=0, \quad y=4 \text { and } y^{\prime}=-2 \text { when } x=0$$

Solve each differential equation. Use the given boundary conditions to find the constants of integration. $$y^{\prime \prime}-2 y^{\prime}=0, \quad y=1+e^{2} \text { and } y^{\prime}=2 e^{2} \text { when } x=1$$

Solve each differential equation. Use the given boundary conditions to find the constants of integration. $$y^{\prime \prime}+2 y^{\prime}+y=0, \quad y=1 \text { and } y^{\prime}=-1 \text { when } x=0$$

Solve each differential equation. Use the given boundary conditions to find the constants of integration. $$y^{\prime \prime}-4 y=0, \quad y=1 \text { and } y^{\prime}=-1 \text { when } x=0$$

Solve each differential equation. Use the given boundary conditions to find the constants of integration. $$y^{\prime \prime}+9 y=0, \quad y=2 \text { and } y^{\prime}=0 \text { when } x=\pi / 6$$

Solve each differential equation. Use the given boundary conditions to find the constants of integration. $$y^{*}+2 y^{\prime}+2 y=0, \quad y=0 \text { and } y^{\prime}=1 \text { when } x=0$$

Solve each differential equation. Use the given boundary conditions to find the constants of integration. $$y^{*}+4 y^{\prime}+13 y=0, \quad y=0 \text { and } y^{\prime}=12 \text { when } x=0$$

Solve each differential equation. $$y^{\prime \prime \prime}-y^{\prime}=0$$

Solve each differential equation. $$y^{2}-3 y^{\prime \prime}-y^{\prime}+3 y=0$$

Solve each differential equation. $$y^{\prime \prime}-7 y^{\prime}+6 y=0$$

Solve each differential equation. $$4 y^{2}-3 y^{\prime}+y=0$$

Solve each differential equation. $$y^{\prime \prime}-y^{\prime \prime}=0$$