Question

Which of the following transformations reduce the differential equation
\[ \frac{dz}{dx} + \frac{1}{x} \log z = \frac{1}{x^2} (\log z)^2 \] into the form \[ \frac{du}{dx} + P(x)\,u = Q(x) \] ?

• A. \( u = (\log z)^{-1} \)
• B. \( u = \log x \)
• C. \( u = (\log 2)^{2} \)
• D. \( u = e^x \)

Hint:

When trying to transform a nonlinear differential equation into a linear form, consider using substitutions such as \( u = (\log z)^{-1} \), which often simplify the equation into a form that is easier to solve.

Answer 1

The Correct Option is A