The differential equation xy' = y(in x – iny) is neither separable, nor linear. by making the substitution y(x) = xv(x), show that the new equation for v(x) equation is separable. n. b. you do not have to actually solve the ode.

We can place everything with v(x) on one side of the equality, everything with x on the other side. This is done on the step-by-step explanation, and shows that the new equation is separable.

Step-by-step explanation:

We have the following differential equation:

We are going to apply the following substitution:

The derivative of y is the derivative of a product of two functions, so

Replacing in the differential equation, we have

Simplifying by x:

Here, we have to apply the following ln property:

So

Simplifying by x,we have:

Now, we can apply the above ln property in the other way:

But

So:

We can place everything that has v on one side of the equality, everything that has x on the other side, so:

This means that the equation is separable.

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.

step-by-step explanation:

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