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Ne4ueva [31]
3 years ago
7

Section 5.2 Problem 9:Find the general solution.

3D%200" id="TexFormula1" title="y'' - 2y' + 3y = 0" alt="y'' - 2y' + 3y = 0" align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
Ira Lisetskai [31]3 years ago
4 0

Answer:

y(x)=C_1e^{-x}+C_2e^{3x}

Step-by-step explanation:

To solve a second-order homogeneous differential equation, we need to substitute each term with the auxiliary equation am^2+bm+c=0 where the values of m are the roots:

y''-2y'+3y=0\\\\m^2-2m+3=0\\\\(m+1)(m-3)=0\\\\m=-1,\:m=3

Since the values of m are distinct real roots, then the general solution is y(x)=C_1e^{m_1x}+C_2e^{m_2x}.

Thus, the general solution for our given differential equation is y(x)=C_1e^{-x}+C_2e^{3x}.

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