Use the concept of a continuous dynamical system .Solve the differential equation . Solvethe system when A is diagonalizable over R,and sketch the phase portrait for 2 × 2 matrices A.
Solve the initial value problems posed in Exercises 1through 5. Graph the solution.
3. with .
The solution is .
Consider the differential equation with initial value (k is an arbitrary constant). The solution is .
The solution of the linear differential equation and is .
Given the differential equation with the initial condition .
Substitute in the solution as follows:
Hence, the solution for the differential equation is .
The graph of the equation is sketched below as follows:
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