1. Tardigrade
  2. Question
  3. Mathematics
  4. The equation of the curve for which the cartesian subtangent varies as the reciprocal of the square of the abscissa, is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The equation of the curve for which the cartesian subtangent varies as the reciprocal of the square of the abscissa, is

Differential Equations

Solution:

Given: Cartesian sub-tangent $\propto \frac{1}{\text { square of abscissa }}$
i.e., $\frac{y}{d y / d x}=\frac{k}{x^{2}}$ or
$\frac{d y}{y}=\frac{x^{2}}{k} d x$
Integrating, $\log y=\frac{x^{3}}{3 k}+\log c$
or $y=c e^{x^{3} / 3 k}$