Solve the given initial value problem. $y''' - 4 y'' + 7 y' - 6 y = 0;$ $y (0) = 1, y' (0) = 0,$ $y'' (0) = 0$

Question

Solve the given initial value problem. $y''' - 4 y'' + 7 y' - 6 y = 0;$ $y (0) = 1, y' (0) = 0,$ $y'' (0) = 0$

Accepted Answer

The solution of the given initial value $y''' - 4 y'' + 7 y' - 6 y = 0$ is $y (t) = \sqrt{2} e^{t} (\sin (\sqrt{2} t)) + e^{2 t}$ when $y (0) = 1, y' (0) = 0$ and $y'' (0) = 0$ .

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Fundamentals Of Differential Equations And Boundary Value Problems

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Solve the given initial value problem. $y''' - 4 y'' + 7 y' - 6 y = 0;$ $y (0) = 1, y' (0) = 0,$ $y'' (0) = 0$

Step by Step Solution

Step 1: Differentiate the value of y.

Step 2: Finding the general solution

Step 3: Substituting the values of y(0)=1,y'(0)=0 and y''(0)=0

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Fundamentals Of Differential Equations And Boundary Value Problems

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Solve the given initial value problem. y'''-4y''+7y'-6y=0;y(0)=1,y'(0)=0,y''(0)=0

Step by Step Solution

Step 1: Differentiate the value of y.

Step 2: Finding the general solution

Step 3: Substituting the values of y(0)=1,y'(0)=0 and y''(0)=0

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Solve the given initial value problem. $y''' - 4 y'' + 7 y' - 6 y = 0;$ $y (0) = 1, y' (0) = 0,$ $y'' (0) = 0$