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:

`(dy)/(dx)=(y)/(x)\\\\=(dy)/(y)=(dx)/(x)\\\\\int (dy)/(y)=\int (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* 1\\\\\therefore c=-2\\`

Thus solution becomes

`y=-2x`