Question

Dy/dx = y/x , y(1) = −2

Answer 1

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

$y=-2x$