### Home > CALC > Chapter 7 > Lesson 7.3.5 > Problem 7-162

7-162.

No calculators! Suppose . Homework Help ✎ Find the particular solution of this differential equation containing the point (0,3).

If you have not already done so, solve your equation for

*y*.Find the domain and range of your equation.

Cross multiply in order to separate the variables.

Integrate both sides.

Solve for *C* by evaluating the given point.

*y* = ln(*x*^{3} + *e*^{3})

The domain is the set of values *x* can be so that *y* is still defined.

The range is the set of *y* values resulting from inputting all members of the domain in the function.

The domain of the parent graph, *y* = ln*x*, is *x* > 0.