Browse Questions

# Solve the following $yx^{2}dx+e^{-x}dy=0$

Toolbox:
• First order , first degree DE
• Variable separable : Variables of a DE are rearranged to separate then, ie
• $f_1(x)g_2(y)dx+f_2(x)g_1(y)dy=0$
• Can be written as $\large\frac{g_1 (y)}{g_2(y)}$$dy=-\large\frac{f_1(x)}{f_2(x)}$$dx$
• The solution is therefore $\int \large\frac{g_1(y)}{g_2(y)}$$dy=-\int \large\frac{f_1(x)}{f_2(x)}$$dx+c$
Step 1:
$yx^2dx+e^{-x}dy=0$ divided by $ye^{-x}$
$\large\frac{x^2}{e^{-x}}$$dx+\large\frac{dy}{y}$$=0$
Step 2:
The variable are separated