  ### Home > CALC > Chapter 7 > Lesson 7.3.2 > Problem7-120

7-120.

Find the antiderivative of the following differential equations. Use implicit integration when necessary. Solve your equations for $y$. Be careful about introducing the constant of integration at the appropriate time.

1. $\frac { d y } { d x }= 7x + 3$

Notice that the derivative is in terms of $x$. Antidifferentiate!

1. $\frac { d y } { d x }= 7y + 3$

Compare and contrast part (a) with part (b).
Which one requires implicit integration?

1. $\frac { d y } { d x }= 7y^2$

Translation: The derivative is equal the the original function squared times a constant.
What can you conclude about the original function?
Is it linear, quadratic, cubic, exponential, trigonometric...?
Use implicit integration to check your conjecture.

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

Translation: The derivative of this function is a constant.
What can you conclude about the function?

1. $\frac { d y } { d x }= e^y$

$y = −\operatorname{ln}|−x + C|$
Explain the significance of the absolute value.