CPM Homework Help : CALC Problem 7-120

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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.

$\frac { d y } { d x }= 7x + 3$
Hint (a):
Notice that the derivative is in terms of $x$ . Antidifferentiate!

$\frac { d y } { d x }= 7y + 3$
Hint (b):
Compare and contrast part (a) with part (b).
Which one requires implicit integration?

$\frac { d y } { d x }= 7y^2$
Hint (c):
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.

$\frac { d y } { d x }= 7$
Hint (d):
Translation: The derivative of this function is a constant.
What can you conclude about the function?

$\frac { d y } { d x }= e^y$
Answer (e):
$y = −\operatorname{ln}|−x + C|$
Explain the significance of the absolute value.

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