Question

If $m$ and $n$ are degree and order of $(1+y_1^2)^{2/3}=y_2$, then the value of $\frac {m+n}{m-n}$ is

• A. 3
• B. 4
• C. 5
• D. 2

Answer 1

Answer: (C)

Given differential equation is
$\left(1+\left(\frac{d y}{d x}\right)^{2}\right)^{2 / 3}=\left(\frac{d^{2} y}{d x^{2}}\right)$
$\Rightarrow \left(1+\left(\frac{d y}{d x}\right)^{2}\right)^{2}=\left(\frac{d^{2} y}{d x^{2}}\right)^{3}$
Now, Order $=n=2$
Degree $=m=3$
Then, $\frac{m+n}{m-n}=\frac{3+2}{3-2}=5$