dx2/dx1 = x2(-3 + x1) / (x1 (-3 + 4x2) how do you solve by separating DE method?

Question

zehanz · Answer

Assuming $x_1$ and $x_2$ are your variables, cross-multiplication is the first step:

$x_1(-3+4x_2)dx_2=x_2(-3+x_1)dx_1$.

Now divide by $x_1$  and $x_2$:

$\dfrac{-3+4x_2}{x_2}dx_2=\dfrac{-3+x_1}{x_1}dx_1$

Variables are separated now.

zehanz · Answer

To solve, you'd better split the fractions like this:$$\int\limits \left(\frac{-3}{x_2}+4\right)dx_2=\int\limits \left(\frac{-3}{x_1}+1\right)dx_1+C$$This will be equal to:$$-3 \ln|x_2|+4x_2=-3 \ln|x_1|+x_1+C$$

To get $x_2$ as a function of $x_1$ from this formula doesn't look easy though...

anonymous · Answer

Thank you!!! i get it now!!

zehanz · Answer

YW!