### Home > CALC > Chapter 7 > Lesson 7.3.2 > Problem 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. Homework Help ✎= 7 *x*+ 3= 7 *y*+ 3= 7 *y*^{2}= 7 = *e*^{y}

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

Compare and contrast part (a) with part (b).

Which one requires implicit integration?

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.

Translation: The derivative of this function is a constant.

What can you conclude about the function?

*y* = −ln|−*x* + *C*|

Explain the significance of the absolute value.