## Related questions with answers

Question

Use integration to find a general solution of the differential equation.

$dy/dx = e^2-^x)$

Solutions

VerifiedSolution A

Solution B

Answered 7 months ago

Step 1

1 of 6In this exercise, for the given initial condition, we will find the particular solution of the differential equation.

*Which method can we apply to solve this differential equation?*

Answered 7 months ago

Step 1

1 of 2$\begin{align*} \text{We have:} \\\frac{dy}{dx}&=e^{2-x} \\\\ \text{\textbf{Multuply} by $dx$:} \\ dy &= e^{2-x}dx \\ \text{\textbf{Integrate} both sides:} \\ \int dy &= \int e^{2-x}dx \\ \text{Let it be:} \\2-x&= u \\\\ \text{\textbf{Integrate} both sides:} \\ -dx &= du \\ \text{Now, we have:} \\ \int dy &= \int e^u(-du) \\ y&= -e^u + C \\ \text{\textbf{Substitute} $u=2-x$:}\\ y&=\boxed{ -e ^ {2-x} + C} \end{align*}$

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