Q120 / 160 · AP EAMCET 2024 (22 May Shift 1) · Mathematics
The sum of the order and degree of the differential equation $x\left(\frac{d^2 y}{d x^2}\right)^{\frac{1}{2}}=\left(1+\frac{d y}{d x}\right)^{\frac{4}{3}}$ is
- Correct answerA5
- B8
- C12
- D10
Solution
$x\left(\frac{d^2 y}{d x^2}\right)^{1 / 2}=\left(1+\frac{d y}{d x}\right)^{4 / 3}$
Squaring both sides $x^2\left(\frac{d^2 y}{d x^2}\right)=\left(1+\frac{d y}{d x}\right)^{8 / 3}$
Cubing both sides $x^6\left(\frac{d^2 y}{d x^2}\right)^3=\left(1+\frac{d y}{d x}\right)^8$
So, degree $=3$, order $=2 \Rightarrow$ Sum $=3+2=5$.
Squaring both sides $x^2\left(\frac{d^2 y}{d x^2}\right)=\left(1+\frac{d y}{d x}\right)^{8 / 3}$
Cubing both sides $x^6\left(\frac{d^2 y}{d x^2}\right)^3=\left(1+\frac{d y}{d x}\right)^8$
So, degree $=3$, order $=2 \Rightarrow$ Sum $=3+2=5$.
Hence, the correct answer is option: 'A'.