What is a solution to the differential equation $(x^{2}) (e^{y}) \frac{d y}{d x} = 4$ $(x^2)(e^y)dy/dx=4$ ?

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What is a solution to the differential equation $(x^{2}) (e^{y}) \frac{d y}{d x} = 4$ $(x^2)(e^y)dy/dx=4$ ?

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Answer 1 · 2016-08-02T03:18:56

$y = ln (C - \frac{4}{x})$ $y=ln(C-4/x)$

Explanation:

We can separate the variables:

$x^{2} e^{y} \frac{d y}{d x} = 4 \Rightarrow e^{y} d y = 4 x^{- 2} d x$ $x^2e^ydy/dx=4" "=>" "e^ydy=4x^-2dx$

Integrate both sides:

$\int e^{y} d y = 4 \int x^{- 2} d x \Rightarrow e^{y} = - \frac{4}{x} + C \Rightarrow y = ln (C - \frac{4}{x})$ $inte^ydy=4intx^-2dx" "=>" "e^y=-4/x+C" "=>" "y=ln(C-4/x)$

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What is a solution to the differential equation $(x^{2}) (e^{y}) \frac{d y}{d x} = 4$ $(x^2)(e^y)dy/dx=4$ ?

1 Answer

Explanation:

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What is a solution to the differential equation (x^2)(e^y)dy/dx=4(x2)(ey)dydx=4(x^2)(e^y)dy/dx=4?

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What is a solution to the differential equation $(x^{2}) (e^{y}) \frac{d y}{d x} = 4$ $(x^2)(e^y)dy/dx=4$ ?