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Gemiola [76]
3 years ago
12

Section 5.2 Problem 7:Find the general solution

3D%200" id="TexFormula1" title="y'' - 8y' + 16y = 0" alt="y'' - 8y' + 16y = 0" align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
nalin [4]3 years ago
8 0

Answer:

y(x)=C_1e^{4x}+C_2e^{4x}

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''-8y'+16y=0\\\\m^2-8m+16=0\\\\(m-4)^2=0\\\\m-4=0\\\\m=4

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

Thus, the general solution for our given differential equation is y(x)=C_1e^{4x}+C_2e^{4x}

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