KCET · Maths · Differential Equations
The order and degree of the differential equation \(\left[1+\left(\frac{d y}{d x}\right)^{5}\right]^{\frac{1}{3}}=\frac{d^{2} y}{d x^{2}}\) are respectively
- A 1,5
- B 2,1
- C 2,5
- D 2,3
Answer & Solution
Correct Answer
(D) 2,3
Step-by-step Solution
Detailed explanation
Given differential equation is
\[
\left[1+\left(\frac{d y}{d x}\right)^{5}\right]^{1 / 3}=\frac{d^{2} y}{d x^{2}}
\]
On cubing both sides, we get
\[
1+\left(\frac{d y}{d x}\right)^{5}=\left(\frac{d^{2} y}{d x^{2}}\right)^{3}
\]
Now, order is 2 and degree is 3 .
\[
\left[1+\left(\frac{d y}{d x}\right)^{5}\right]^{1 / 3}=\frac{d^{2} y}{d x^{2}}
\]
On cubing both sides, we get
\[
1+\left(\frac{d y}{d x}\right)^{5}=\left(\frac{d^{2} y}{d x^{2}}\right)^{3}
\]
Now, order is 2 and degree is 3 .
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