Joanna Benson
2022-01-18
Answered

Solve: $y{}^{\u2033}+2{y}^{\prime}-3y=0$

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sukljama2

Answered 2022-01-19
Author has **33** answers

puhnut1m

Answered 2022-01-20
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alenahelenash

Answered 2022-01-24
Author has **368** answers

Start by finding the characteristic polynomial. In this case it is ${x}^{2}+2x-3$ . Find its zeros; they are $x=-3,1$ . The general solution to your differential equation is $c{e}^{{x}_{i}t}$ , where ${x}_{i}$ is a root to your characteristic polynomial. So we have two linearly independent solutions; $y={e}^{-3t},y={e}^{1t}$ . Because this is a linear differential equation, we can take any linear combo of those two solutions, and that will also be a solution. So the general solution for y is $y(t)={c}_{1}{e}^{-3t}+{c}_{2}{e}^{1t}$ where ${c}_{1}\text{}\text{and}\text{}{c}_{2}$ are determined by your initial conditions $(y(0)\text{}and\text{}{y}^{\prime}(0))$

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