#higher derivatives

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Differential Equations

What are the order and degree, respectively, of the differential equation ( d^3ydx^3 )^2 = y^4 + ( dydx )^5?

Let's break it down: we verify 3, 2 by full calculation: use standard identity, substitute, simplify step by step to reach 3, 2.

Ref: NCERT Mathematics Class XII — Differential Equations

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Differential Equations

The order and degree of the differential equation ( d^4ydx^4 )^1/2 = [ 1 + ( d^2ydx^2 )^2 ]^1/3 respectively are

Understanding this is easy: solving fully: apply relevant formula, put numbers, compute. Result comes as 4, 3. Easy verification shows it satisfies condition.

Ref: NCERT Mathematics Class XII — Differential Equations

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#higher derivatives

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What are the order and degree, respectively, of the differential equation ( d^3ydx^3 )^2 = y^4 + ( dydx )^5?

The order and degree of the differential equation ( d^4ydx^4 )^1/2 = [ 1 + ( d^2ydx^2 )^2 ]^1/3 respectively are

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