- #1

karush

Gold Member

MHB

- 3,269

- 5

2000

(a) Find the solution of the given

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

\begin{align*}\displaystyle

xdx&=-ye^{-x}dy \\

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

xe^x\, dx&=-y\, dy

\end{align*}

(b) Plot the

$\quad \textit{ok... I tried some attempts in W|A but my input didn't work}\\$

(c) Determine (at least approximately) the

$\quad \textit{...provided by initial value!}$

(a) Find the solution of the given

**initial value**problem in explicit form.$$xdx+ye^{-x}dy=0, \quad y(0)=1$$

\begin{align*}\displaystyle

xdx&=-ye^{-x}dy \\

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

xe^x\, dx&=-y\, dy

\end{align*}

(b) Plot the

**graph**of the solution$\quad \textit{ok... I tried some attempts in W|A but my input didn't work}\\$

(c) Determine (at least approximately) the

**interval**in which the solution is defined.$\quad \textit{...provided by initial value!}$

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