The given differential equation is (x-y^3)dy + y dx = 0.

First, we rewrite the equation in the standard form of a first order linear differential equation, which is dy/dx + P(x)y = Q(x).

So, we can rewrite the equation as dy/dx + y/x = y^3.

Here, P(x) = 1/x and Q(x) = y^3.

The integrating factor is e^(∫P(x) dx).

So, the integrating factor is e^(∫1/x dx) = e^(ln|x|) = |x|.

Therefore, the integrating factor for the solution of the given differential equation is |x|.

Question

The given differential equation is (x-y^3)dy + y dx = 0.

First, we rewrite the equation in the standard form of a first order linear differential equation, which is dy/dx + P(x)y = Q(x).

So, we can rewrite the equation as dy/dx + y/x = y^3.

Here, P(x) = 1/x and Q(x) = y^3.

The integrating factor is e^(∫P(x) dx).

So, the integrating factor is e^(∫1/x dx) = e^(ln|x|) = |x|.

Therefore, the integrating factor for the solution of the given differential equation is |x|.

Knowee AI · Accepted Answer

The given differential equation is (x-y^3)dy + y dx = 0.

First, we rewrite the equation in the standard form of a first order linear differential equation, which is dy/dx + P(x)y = Q(x).

So, we can rewrite the equation as dy/dx + y/x = y^3.

Here, P(x) = 1/x and Q(x) = y^3.

The integrating factor is e^(∫P(x) dx).

So, the integrating factor is e^(∫1/x dx) = e^(ln|x|) = |x|.

Therefore, the integrating factor for the solution of the given differential equation is |x|.

Integrating factor for the solution of differential equation (x-y3)dy + y dx = 0 is