Question

x dy + (y + 4) dx=0 solve the ode in linear ​

Answer 1

Answer:

Step-by-step explanation:

Let’s rewrite it into xdy=ydx

dividing both sides by xy,

dy/y=dx/x

Let us integrate both sides,

lny = lnx + c

where c is any arbitrary real number (constant). Here , I have applied the fact that integrating 1/y gives us lny

For simplicity, let us rewrite our constant c into lnc. The range of lnc is also all real numbers, so it won't make a difference.

lny = lnx + lnc

=> lny = ln(c.x)

applied the identity lna + lnb = ln(ab)

we can hence simplify it into y=cx

This is the required solution. We can rewrite the same answer as

y/x = c

x/y = c (I will not prefer these two since they are not defined if the denominator is 0)

x=cy

If you want to find the integration constant c, any point (where x and y are given) should be specified so that on substituting the values of x and y, we can find c.

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