Find the specific solution of the differential equation dy/dx= 4y/x^2 with condition y(-4)=1 A. y=-1-4/x B. y=-e^1/x C.y=e^(-4/x) D. None of these

Question

asked Dec 5, 2020 159k views

1 Answer

Riegersn · Answer 1 · 2020-12-09T20:03:56+0000

This ODE is separable:

$(\mathrm dy)/(\mathrm dx)=(4y)/(x^2)\implies\frac{\mathrm dy}y=\frac4{x^2}\,\mathrm dx$

Integrating both sides gives

$\ln|y|=-\frac4x+C$

Given the initial condition
y(-4)=1 we find

$\ln|1|=-\frac4{-4}+C\implies C=-1$

so that the particular solution is

$\ln|y|=-\frac4x-1$

$\implies y=e^(-(1+4/x)))$

so the answer is D.