Which of the following is equivalent to \(e^{x+y}\)?

Which if the following is equivalent to \(e^{x-y}\)

Select the correct answers to the following

Select the correct answers to the following

Select the correct answers to the following

Following an integration, the result is simplified. Decide whether the second statement is a correct simplification of the first one, given that \(\large c\) and \(\large c_1\) are arbitrary constants

Following an integration, the result is simplified. Decide whether the second statement is a correct simplification of the first one, given that \(\large c\) and \(\large c_1\) are arbitrary constants

Following an integration, the result is simplified. Decide whether the second statement is a correct simplification of the first one, given that \(\large c\) and \(\large c_1\) are arbitrary constants

Following an integration, the result is simplified. Decide whether the second statement is a correct simplification of the first one, given that \(\large c\) and \(\large c_1\) are arbitrary constants

Following an integration, the result is simplified. Decide whether the second statement is a correct simplification of the first one, given that \(\large c\) and \(\large c_1\) are arbitrary constants

Following an integration, the result is simplified. Decide whether the second statement is a correct simplification of the first one, given that \(\large c\) and \(\large c_1\) are arbitrary constants

Following an integration, the result is simplified. Decide whether the second statement is a correct simplification of the first one, given that \(\large c\) and \(\large c_1\) are arbitrary constants

Following an integration, the result is simplified. Decide whether the second statement is a correct simplification of the first one, given that \(\large c\) and \(\large c_1\) are arbitrary constants

Following an integration, the result is simplified. Decide whether the second statement is a correct simplification of the first one, given that \(\large c\) and \(\large c_1\) are arbitrary constants

Following an integration, the result is simplified. Decide whether the second statement is a correct simplification of the first one, given that \(\large c\) and \(\large c_1\) are arbitrary constants

How does the following differential equation separate?

\(\large \frac{\text{d}y}{\text{d}x}=e^{x+y}\)

How does the following differential equation separate?

\(\large \frac{\text{d}y}{\text{d}x}=sin({xy})\)

Here is a solution to a differential equation. Is the work all correct? If not, which step is wrong?

\(\large \quad \quad\quad \quad \quad \quad \frac{\text{d}y}{\text{d}x}=\frac{x^2+1}{2y}\)

\(\large \text{step 1} \quad \quad \int {2y}\ {\text{d}y}=\int (x^2+1 )\ {\text{d}x} \)

\(\large \text{step 2} \quad \quad y^2=\frac{x^3}{3}+x+c \)

\(\large \text{step 3} \quad \quad y=\pm\sqrt{\frac{x^3}{3}+x+c}\)

Here is a solution to a differential equation. Is the work all correct? If not, which step is wrong?

\(\large \quad \quad\quad \quad \quad \quad \frac{\text{d}y}{\text{d}x}=\frac{lnx}{y}\)

\(\large \text{step 1} \quad \quad \int {y}\ {\text{d}y}=\int lnx\ {\text{d}x} \)

\(\large \text{step 2} \quad \quad y^2=xlnx-x+c \)

\(\large \text{step 3} \quad \quad y=\pm\sqrt{xlnx-x+c}\)

Here is a solution to a differential equation. Is the work all correct? If not, which step is wrong?

\(\large \quad \quad\quad \quad \quad \quad \frac{\text{d}y}{\text{d}x} = -xe^y\)

\(\large \text{step 1} \quad \quad \int {e^{-y}}\ {\text{d}y}=\int -x\ {\text{d}x} \)

\(\large \text{step 2} \quad \quad -e^{-y}=- \frac{x^2}{2}+c\)

\(\large \text{step 3} \quad \quad e^{-y}= \frac{x^2}{2}+c_1\)

\(\large \text{step 4} \quad \quad {-y}= ln({\frac{x^2}{2}+c_1)}\)

\(\large \text{step 5} \quad \quad {y}= ln({-\frac{x^2}{2}+c_2)}\)

Here is a solution to a differential equation. Is the work all correct? If not, which step is wrong?

\(\quad \quad \quad \quad \large \frac{\text{d}y}{\text{d}x}=e^{x-y}\)

\(\large \text{step 1} \quad \quad \frac{\text{d}y}{\text{d}x}=e^{x} \cdot e^{-y}\)

\(\large \text{step 2} \quad \quad \int {e^{-y}}\ {\text{d}y}=\int e^{x}\ {\text{d}x} \)

\(\large \text{step 3} \quad \quad -e^{-y}=e^{x}+c\)

\(\large \text{step 4} \quad \quad e^{-y}=-e^x+c_1\)

\(\large \text{step 5} \quad \quad y=-ln(-e^x+c_1)\)

Which of the following is the correct solution to the following differential equation

\(\quad \quad \quad \quad \large \frac{\text{d}y}{\text{d}x}=y\)

Which of the following is the correct solution to the following differential equation

\(\quad \quad \quad \quad \large \frac{\text{d}y}{\text{d}x}=3x^2y\)

Which of the following is the correct solution to the following differential equation

\(\quad \quad \quad \quad \large \frac{\text{d}y}{\text{d}x}=\frac{x}{y}\)

Which of the following is the correct solution to the following differential equation

\(\quad \quad \quad \quad \large \frac{\text{d}y}{\text{d}x}=\frac{sec^2x}{sec\ y}\)