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Separating variable in the equation gives you the following equation:​

Separating variable in the equation gives you the following equation:​-example-1
User RavenMan
by
8.2k points

2 Answers

6 votes

Answer: E

Explanation:


ye^(-x) (dy)/(dx)=x\\\\y (dy)/(dx)=xe^(x) \\ \\ \boxed{y dy=xe^(x) dx}

User Lyda
by
8.0k points
2 votes

Answer:


\textsf{E.} \quad y\:dy=xe^x\:dx

Explanation:

Given equation:


ye^(-x)(dy)/(dx)=x

Divide both sides by
e^(-x):


\implies (ye^(-x))/(e^(-x))\:(dy)/(dx)=(x)/(e^(-x))


\implies y\:(dy)/(dx)=(x)/(e^(-x))

Multiply both sides by
dx :


\implies y\:(dy)/(dx)\cdot dx=(x)/(e^(-x))\cdot dx


\implies y\:dy=(x)/(e^(-x))\:dx


\textsf{Apply exponent rule} \quad (1)/(a^(-n))=a^n:


\implies y\:dy=xe^x\:dx

User Wolfram Rittmeyer
by
7.7k points

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