• :00Days
• :00Hours
• :00Mins
• 00Seconds
A new era for learning is coming soon

Suggested languages for you:

Americas

Europe

Q. 63

Expert-verified
Found in: Page 945

### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

# Solve the exact differential equations in Exercises 63–66. ${e}^{y}+\left(x{e}^{y}-7\right)\frac{dy}{dx}=0$

The solution of given exact differential equation is: $x{e}^{y}-7y+C=0$

See the step by step solution

## Step 1. Given information

Exact differential equation, ${e}^{y}+\left(x{e}^{y}-7\right)\frac{dy}{dx}=0$

## Step 2. Solving the given exact differential equation

$\mathrm{Given},{e}^{y}+\left(x{e}^{y}-7\right)\frac{dy}{dx}=0\phantom{\rule{0ex}{0ex}}⇒{e}^{y}dx+\left(x{e}^{y}-7\right)dy=0\phantom{\rule{0ex}{0ex}}\mathrm{It}\mathrm{is}\mathrm{a}\mathrm{exact}\mathrm{differential}\mathrm{equation}\mathrm{of}\mathrm{the}\mathrm{the}\mathrm{form}Mdx+Ndy=0,\phantom{\rule{0ex}{0ex}}\mathrm{with}\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}.\mathrm{the}\mathrm{solution}\mathrm{is}\mathrm{given}\mathrm{by},\phantom{\rule{0ex}{0ex}}f\left(x,y\right)=\int \left(\mathrm{treating}yas\mathrm{constant}\mathrm{in}\mathrm{M}\right)dx+\int \left(\mathrm{terms}\mathrm{independent}\mathrm{of}x\mathrm{in}N\right)dy=0\phantom{\rule{0ex}{0ex}}⇒\int {e}^{y}dx+\int \left(-7\right)dy=0\phantom{\rule{0ex}{0ex}}⇒x{e}^{y}-7y+C=0$