### Home > APCALC > Chapter 7 > Lesson 7.3.1 > Problem7-100

7-100.

Solve each of the following differential equations. Use implicit integration when necessary. Solve your equations for $y$. Verify that your answers are correct by differentiation.

1.  $\frac { d y } { d x }= 7x$

$y = \text{ _______} + C$

1. $\frac { d y } { d x }= 7y$

Translation: The derivative of $y$ is $y$ times a constant.
What is $y$?

1. $\frac { d y } { d x }= e^{−y}$

Translation: The derivative of $y$ is $e^{− y}$. What is $y$?

Will absolute value symbols be part of the solution?
Why or why not?

$\frac{dy}{dx}=\frac{1}{e^{y}}$

$e^{y}dy = dx$

$\int e^{y}dy=\int dx\ \ \text{ Now solve for }y.$