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. Homework Help ✎

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 ey. 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

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