Question

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

Answer 1

Answer: E

Explanation:

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

Answer 2

`\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`