#### Arman777

Gold Member

- 1,613

- 128

Cauchy-Euler is a type of diff equation which is described by

$$a_0x^2(\frac {d^2y} {dx^2})+a_1x(\frac {dy} {dx})+a_2y=F(x)$$

The transformation of ##x=e^t## can solve the equation.

Now, in here I didnt understand how to transform ##\frac {dy} {dx}## to ##\frac {dy} {dt}##.

it goes like this ##\frac {dy} {dx}=\frac {dy} {dt} \frac {1} {x}## and then I am stuck I should take another derivative but I couldnt do it somehow.

$$a_0x^2(\frac {d^2y} {dx^2})+a_1x(\frac {dy} {dx})+a_2y=F(x)$$

The transformation of ##x=e^t## can solve the equation.

Now, in here I didnt understand how to transform ##\frac {dy} {dx}## to ##\frac {dy} {dt}##.

it goes like this ##\frac {dy} {dx}=\frac {dy} {dt} \frac {1} {x}## and then I am stuck I should take another derivative but I couldnt do it somehow.

Last edited: