MHT CET · Maths · Differential Equations
The order and degree of the differential equation \(\sqrt{1+\frac{1}{\left(\frac{d y}{d x}\right)^{2}}}=\left(\frac{d^{2} y}{d x^{2}}\right)^{\frac{3}{2}}\) are respectively
- A 3,2
- B 2,3
- C 2,2
- D 3,3
Answer & Solution
Correct Answer
(B) 2,3
Step-by-step Solution
Detailed explanation
(A)
By raising the given equation to the power of 2 , we get
\(\begin{aligned}
& 1+\frac{1}{\left(\frac{d y}{d x}\right)^{2}}=\left(\frac{d^{2} y}{d x^{2}}\right)^{3} \\
\therefore &\left(\frac{d y}{d x}\right)^{2}+1=\left(\frac{d^{2} y}{d x^{2}}\right)^{3}\left(\frac{d y}{d x}\right)^{2}
\end{aligned}\)
It's order is 2 and degree is 3 .
By raising the given equation to the power of 2 , we get
\(\begin{aligned}
& 1+\frac{1}{\left(\frac{d y}{d x}\right)^{2}}=\left(\frac{d^{2} y}{d x^{2}}\right)^{3} \\
\therefore &\left(\frac{d y}{d x}\right)^{2}+1=\left(\frac{d^{2} y}{d x^{2}}\right)^{3}\left(\frac{d y}{d x}\right)^{2}
\end{aligned}\)
It's order is 2 and degree is 3 .
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