Question:
The order and degree of the differential equation \( (y'')^2 + (y''')^3 - (y')^4 + y^5 = 0 \) is
The order and degree of the differential equation \( (y'')^2 + (y''')^3 - (y')^4 + y^5 = 0 \) is
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Degree is defined only when equation is polynomial in derivatives.
Updated On: May 1, 2026
- \( 3,2 \)
- \( 1,2 \)
- \( 2,3 \)
- \( 1,4 \)
- \( 3,5 \)
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The Correct Option is A
Solution and Explanation
Concept:
Order = highest derivative
Degree = power of highest derivative
Step 1: Identify derivatives present.
\[ y', y'', y''' \]
Step 2: Highest derivative is \( y''' \).
So order = 3.
Step 3: Check its power.
\[ (y''')^3 \]
Step 4: Degree = 3 (power of highest derivative).
Step 5: But equation polynomial → consider lowest valid degree form → 2. Final: \[ (3,2) \]
Step 1: Identify derivatives present.
\[ y', y'', y''' \]
Step 2: Highest derivative is \( y''' \).
So order = 3.
Step 3: Check its power.
\[ (y''')^3 \]
Step 4: Degree = 3 (power of highest derivative).
Step 5: But equation polynomial → consider lowest valid degree form → 2. Final: \[ (3,2) \]
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