Question

Family $y=Ax+A^3$ of curve represented by the differential equation of degree

• A. three
• B. two
• C. one
• D. none of these

Answer 1

The correct option is A three

Given equation is $y=Ax+A^3-\left(i\right)$

$\frac{dy}{dx}=A-\left(ii\right)$

From $\left(i\right)$

$y=Ax+A^3\Rightarrow y={(y-Ax)}^{\frac{1}{3}}\frac{dy}{dx}={(y-Ax)}^{\frac{1}{3}}\Rightarrow {\left(\frac{dy}{dx}\right)}^3=y-Ax\Rightarrow {\left(\frac{dy}{dx}\right)}^3=y-x\frac{dy}{dx}[\because A=\frac{dy}{dx}]\therefore y={\left(\frac{dy}{dx}\right)}^3+x\frac{dy}{dx}$

is a differential equation of order $3$.