The number of arbitrary constants in the general solution of a differential equationof fourth order are:(A) 0 (B) 2 (C) 3 (D) 4

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Text solutionVerified

Solution: General equation of 4th order is

\frac{d ^{4} y}{d x ^{4}} = k

\frac{d ^{3} y}{d x ^{3}} = k x + c 1

\frac{d ^{2} y}{d x ^{2}} = k \frac{x ^{2}}{2} + c 1 x + c 2

\frac{d y}{d x} = k \frac{x ^{3}}{6} + (c 1) \frac{x ^{2}}{2} + c 2 x + c 3

y = k \frac{x ^{4}}{24} + (c 1) \frac{x ^{3}}{6} + c 2 \frac{x ^{2}}{2} + c 3 x + c 4

Number of arbitrary constant=

4

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Question Text	The number of arbitrary constants in the general solution of a differential equationof fourth order are:(A) 0 (B) 2 (C) 3 (D) 4
Answer Type	Text solution:1
Upvotes	150