Practice: Solving ODE by separation of variables

Calculus Level 2

What is the solution of the ordinary differential equation $y = x \frac{dy}{dx} \ln x$ that satisfies $y(3)=\ln 81?$

y=3\text{ln}x+x

y=\text{ln}(x+{x}^{2})

y=4 \text{ln}x

y=2\text{ln}({x}^{3}+2{x}^{2})

1 solution

Hjalmar Orellana Soto
Dec 23, 2016

$\frac{dy}{y}=\frac{dx}{x\cdot \ln(x)} \Rightarrow \ln(y)=\ln(\ln(x))+C$ $y=C\cdot \ln(x)$ Using the initial value we have $\ln(81)=C\ln(3) \Rightarrow C=4$ $\Rightarrow y=4\ln(x)$

Practice: Solving ODE by separation of variables

1 solution

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