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Ahat [919]
4 years ago
9

Dy/dx = y/x , y(1) = −2

Mathematics
1 answer:
Arisa [49]4 years ago
8 0

Answer with Step-by-step explanation:

The given differential equation is variable separable in nature and hence will be solved accordingly as follows:

\frac{dy}{dx}=\frac{y}{x}\\\\=\frac{dy}{y}=\frac{dx}{x}\\\\\int \frac{dy}{y}=\int \frac{dx}{x}\\\\ln(y)=ln(x)+ln(c)\\\\ln(y)=ln(cx)\\\\(\because ln(ab)=ln(a)+ln(b))\\\\\therefore y=cx

where 'c' is constant of integration whose value shall be obtained using the given condition y(1)=-2

Thus we have

-2=c\times 1\\\\\therefore c=-2\\

Thus solution becomes

y=-2x

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