KCET · Maths · Differential Equations
The sum of the degree and order of the differential equation \(\left(1+y_1^2\right)^{2 / 3}=y_2\) is
- A 4
- B 6
- C 5
- D 7
Answer & Solution
Correct Answer
(C) 5
Step-by-step Solution
Detailed explanation
\(\left(1+y_1^2\right)^{2 / 3}=y_2\)
\[
\Rightarrow \quad\left[\left(1+y_1^2\right)^{2 / 3}\right]^3=\left(y_2\right)^3 \Rightarrow\left(1+y_1^2\right)^2=y_2^3
\]
Here, highest derivative is \(y_2\).
Therefore, order is 2 and power of \(y_2\) is 3 .
So, the degree is 3 .
Hence, required sum \(=2+3=5\)
\[
\Rightarrow \quad\left[\left(1+y_1^2\right)^{2 / 3}\right]^3=\left(y_2\right)^3 \Rightarrow\left(1+y_1^2\right)^2=y_2^3
\]
Here, highest derivative is \(y_2\).
Therefore, order is 2 and power of \(y_2\) is 3 .
So, the degree is 3 .
Hence, required sum \(=2+3=5\)
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