Q119 / 160 · TS EAMCET 2024 (10 May Shift 2) · Mathematics
The order and degree of the differential equation $\frac{d y}{d x}=\left(\frac{d^2 y}{d x^2}+2\right)^{1 / 2}+\frac{d^2 y}{d x^2}+5$ are respectively
- A2,1
- B2,4
- Correct answerC2,2
- D2,3
Solution
$\begin{aligned} & \frac{d y}{d x}=\left(\frac{d^2 y}{d x^2}+2\right)^{\frac{1}{2}}+\frac{d^2 y}{d x^2}+5 \\ & \frac{d y}{d x}-\frac{d^2 y}{d x^2}-5=\left(\frac{d^2 y}{d x^2}+2\right)^{\frac{1}{2}}\end{aligned}$
Squaring both sides
$\begin{aligned} & \left(\frac{d y}{d x}\right)^2+\left(\frac{d^2 y}{d x^2}\right)^2+25-2 \frac{d y}{d x} \cdot \frac{d^2 y}{d x}-\frac{10 d y}{d x}+\frac{10 d^2 y}{d x^2} \\ & =\frac{d^2 y}{d x^2}+2 \\ & \Rightarrow\left(\frac{d^2 y}{d x^2}\right)^2+\left(\frac{d y}{d x}\right)^2+\frac{9 d^2 y}{d x^2}-\frac{2 d y}{d x} \frac{d^2 y}{d x^2}-\frac{10 d y}{d x}+23=0\end{aligned}$
So, order $=2$, degree $=2$
Hence, the correct answer is option: 'C'.