Sage-Tips

Why degree of sin dy dx is not defined?

sin(dy/dx)=x+y: reason for above to have no defined degree is that sin(x)=x-x^3/3!+

When can you say that a differential equation has no degree?

An equation has no degree or undefined degree if it is not reducible. The determination of the degree of a given differential equation can be very tricky if you are not well versed with the conditions under which the degree of the differential equation is defined.

Why degree is not defined?

Suppose in a differential equation dy/dx = tan (x + y), the degree is 1, whereas for a differential equation tan (dy/dx) = x + y, the degree is not defined. The given differential equation is not a polynomial equation in derivatives. Hence, the degree of this equation is not defined.

What is exponent of differential equation?

Recall that an exponential function is of the form y=ce to the kx. And so we say the general solution of this important differential equation dy dx equals ky is y=ce to the kx, the exponential functions. Same value of k, c would be some other constant, any constant would do.

What is the degree of the differential equation in derivatives?

The differential equation must be a polynomial equation in derivatives for the degree to be defined. Here, the exponent of the highest order derivative is one and the given differential equation is a polynomial equation in derivatives. Hence, the degree of this equation is 1.

How to take the derivatives of a function using logarithms?

Taking the derivatives of some complicated functions can be simplified by using logarithms. This is called logarithmic differentiation. It’s easiest to see how this works in an example. Differentiating this function could be done with a product rule and a quotient rule. However, that would be a fairly messy process.

What is logarithmic differentiation and how does it work?

This is called logarithmic differentiation. It’s easiest to see how this works in an example. Differentiating this function could be done with a product rule and a quotient rule. However, that would be a fairly messy process. We can simplify things somewhat by taking logarithms of both sides. Of course, this isn’t really simpler.

What are the exponential and logarithm functions in calculus?

The most common exponential and logarithm functions in a calculus course are the natural exponential function, ex e x, and the natural logarithm function, ln(x) ln. ⁡. ( x). We will take a more general approach however and look at the general exponential and logarithm function.