### Home > CALC > Chapter 7 > Lesson 7.3.1 > Problem7-108

7-108.

Find the antiderivative of the following differential equations. Use implicit integration when necessary. Solve your equations for $y$. Check your answer by differentiating the result.

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

$y =$ _______ $+ C$

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?

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

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