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- #1

#### karush

##### Well-known member

- Jan 31, 2012

- 2,886

Given #11

$\quad\displaystyle

xdx+ye^{-x}dy=0,\quad y(0)=1$

a. Initial value problem in explicit form.

$\quad xdx=-ye^{-x}dy$

separate

$\quad \frac{x}{e^{-x}}\, dx=-y\, dy$

simplify

$\quad xe^x\, dx=-y\, dy$

rewrite

$\quad y\,dy=-xe^x\,dx$

integrate (with boundaries)

$\quad \int_1^y u\,dy=-\int_0^x ve^v\,dv$

OK i did this so far hopefully ok but didnt know how to do b and c (on desmos)

b. Plot the graph of the solution

c. Interval of solution.

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