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karush
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View attachment 9112
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.
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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