Solve Equation
((dx(t))/dt)=2x(t)+y(t)
((dy(t))/dt)=−3y(t)
(((x^((1)) (t))),((y^((1)) (t))) )= ((2,( 1)),(0,(−3)) ) (((x(t))),((y(t))) )
A= ((2,( 1)),(0,(−3)) )
det{A−𝛌E}=0
det{ ((2,( 1)),(0,(−3)) )− ((𝛌,0),(0,𝛌) )}=0
𝛌=2,−3
v_1 = (((−1)),(( 5)) )
v_2 = ((1),(0) )
((x),(y) )=C_1 e^(λt) v_1 +C_2 e^(λt) v_2 = (((−1),1),(( 5),0) ) (((C_1 e^(2t) )),((C_2 e^(−3t) )) )
((x),(y) )= (((−C_1 e^(2t) +C_2 e^(−3t) )),(( 5C_1 e^(2t) )) )
((dx(t))/dt)=−2C_1 e^(2t) −3C_2 e^(−3t) ≠
2x(t)+y(t)=−2C_1 e^(2t) −2C_2 e^(−3t) +5C_1 e^(2t)
((dy(t))/dt)=10e^(2t) ≠
−3y(t)=−15C_2 e^(2t)
Wrong..... Help
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