CPM Homework Help : APCALC Problem 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.

$\frac { d y } { d x }= 7x$
Hint (a):
$y = \text{ _______} + C$

$\frac { d y } { d x }= 7y$
Hint (b):
Translation: The derivative of $y$ is $y$ times a constant.
What is $y$ ?

$\frac { d y } { d x }= e^{−y}$
Hint (c):
Translation: The derivative of $y$ is $e^{− y}$ . What is $y$ ?
Hint (c):
Will absolute value symbols be part of the solution?
Why or why not?
Step 1(c):
$\frac{dy}{dx}=\frac{1}{e^{y}}$
$e^{y}dy = dx$
Step 2(c):
$\int e^{y}dy=\int dx\ \ \text{ Now solve for }y.$