In each of Problems 1-5, solve the initial value problem and graph the solution. 1. y′′+5y′+6y=3δ(t−2)−4δ(t−5);y(0)=y′(0)=0 2. y′′−4y′+13y=4δ(t−3);y(0)=y′(0)=0 3. y′′′+4y′′+5y′+2y=6δ(t);y(0)=y′(0)=y′′(0)=0 4. y′′+6y′=12δ(t−5π/8);y(0)=3,y′(0)=0 5. y′′+5y′+6y=Bδ(t);y(0)=3,y′(0)=0

Approach: Take the Laplace transform of both sides of the ODE.

Resuelto In each of Problems 1-5, solve the initial value

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In each of Problems 1-5, solve the initial value problem and graph the solution. 1.

y^{''} + 5 y^{'} + 6 y = 3 δ (t - 2) - 4 δ (t - 5); y (0) = y^{'} (0) = 0

y^{''} - 4 y^{'} + 13 y = 4 δ (t - 3); y (0) = y^{'} (0) = 0

y^{'''} + 4 y^{''} + 5 y^{'} + 2 y = 6 δ (t); y (0) = y^{'} (0) = y^{''} (0) = 0

y^{''} + 6 y^{'} = 12 δ (t - 5 π /8); y (0) = 3, y^{'} (0) = 0

y^{''} + 5 y^{'} + 6 y = B δ (t); y (0) = 3, y^{'} (0) = 0