Find the solution of the system of differential equations:
[ x 1 ′ ( t ) x 2 ′ ( t ) ] = [ − 2 + 2 2 + 2 2 − 2 ] . [ x 1 ( t ) x 2 ( t ) ] \displaystyle {\left[\begin{array}{c} {x}_{{1}}'{\left({t}\right)}\\{x}_{{2}}'{\left({t}\right)}\end{array}\right]}={\left[\begin{array}{cc} -{2}&+\frac{{2}}{{2}}\\+\frac{{2}}{{2}}&-{2}\end{array}\right]}.{\left[\begin{array}{c} {x}_{{1}}{\left({t}\right)}\\{x}_{{2}}{\left({t}\right)}\end{array}\right]} [ x 1 ′ ( t ) x 2 ′ ( t ) ] = [ − 2 + 2 2 + 2 2 − 2 ] . [ x 1 ( t ) x 2 ( t ) ]
with initial condition:
[ x 1 ( 0 ) x 2 ( 0 ) ] = [ 3 4 ] \displaystyle {\left[\begin{array}{c} {x}_{{1}}{\left({0}\right)}\\{x}_{{2}}{\left({0}\right)}\end{array}\right]}={\left[\begin{array}{c} {3}\\{4}\end{array}\right]} [ x 1 ( 0 ) x 2 ( 0 ) ] = [ 3 4 ] x 1 ( t ) = \displaystyle {x}_{{1}}{\left({t}\right)}= x 1 ( t ) = Preview Question 6 Part 1 of 2 x 2 ( t ) = \displaystyle {x}_{{2}}{\left({t}\right)}= x 2 ( t ) = Preview Question 6 Part 2 of 2 Submit Try a similar question
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Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c
Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c