Question

The degree of the differential equation $y\left(x\right)=1+\frac{dy}{dx}+\frac{1}{1.2}{\left(\frac{dy}{dx}\right)}^2+\frac{1}{\mathrm{1.2.3}}{\left(\frac{dy}{dx}\right)}^3+.....\frac{1}{\mathrm{1.2.3.......}n}{\left(\frac{dy}{dx}\right)}^n$ is.

• A. $2$
• B. $3$
• C. $1$
• D. n

Answer 1

The correct option is D n

$y\left(x\right)=1+\frac{dy}{dx}+\frac{1}{1\cdot 2}{\left(\frac{dy}{dx}\right)}^2+\cdot \cdot \cdot \cdot \cdot \cdot \cdot$

The last term in the series would be $\frac{1}{n!}(\frac{dy}{dx}{)}^n$

Degree: Power of highest order term

$\Rightarrow$ Power of $\frac{dy}{dx}$ in ${\left(\frac{dy}{dx}\right)}^n=n$