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Oksi-84 [34.3K]
3 years ago
7

Problem 3: Solve the differential equation

le="y' + 2y = 3" alt="y' + 2y = 3" align="absmiddle" class="latex-formula">
​
Mathematics
2 answers:
tatiyna3 years ago
5 0

Answer:

y=Ce^{2x}+\frac{3}{2}

Step-by-step explanation:

y'+2y=3\\\\\frac{dy}{dx}+2y=3\\ \\\frac{dy}{dx}=3-2y\\ \\dy=(3-2y)dx\\\\\frac{1}{3-2y}dy=dx\\ \\\int\limits {\frac{1}{3-2y}dy=\int dx}\\\\\frac{1}{2}ln(|3-2y|)=x+C\\\\ln(|3-2y|)=2x+C\\\\3-2y=e^{2x+C}\\\\3-2y=Ce^{2x}\\\\-2y=Ce^{2x}-3\\\\y=-\frac{Ce^{2x}}{2}+\frac{3}{2}\\ \\y=Ce^{2x}+\frac{3}{2}

Ludmilka [50]3 years ago
4 0

Answer:

Step-by-step explanation:

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