Question

Give the largest interval over which the general solution of Problem 42 is defined.

Short answer

The solution is$x\in (4,\infty )$

Step-by-step solution

Given information

$y\left(x\right)=c_1(x-4{)}^3+c_2(x-4{)}^{3}ln(x-4)$

Solution

From the entire solution of the problem (42), we have its general solution as

$y\left(x\right)=c_1(x-4{)}^3+c_2(x-4{)}^{3}ln(x-4)$

For this solution to be defined, (x-4) should be a positive number since ln(-ve) is not defined.

$$\begin{gathered} x-4>0 \\ x>4 \end{gathered}$$

Then we have

$x\in (4,\infty )$

Conclusion

The final solution is$x\in (4,\infty )$