Ex 9.2, 11 - Number of arbitrary constants in general solution - Gen and Particular Solution

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  1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise
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Ex 9.2, 11 The number of arbitrary constants in the general solution of a differential equation of fourth order are : (A) 0 (B) 2 (C) 3 (D) 4 Let 𝑦﷮′′′′﷯=1 Integrating Both Sides , we get 𝑦﷮′′′﷯=𝑥+𝑐1 Again Integrating 𝑦﷮′′﷯= 𝑥﷮2﷯﷮2﷯+𝑐1𝑥+𝑐2 Again Integrating 𝑦﷮′﷯= 𝑥﷮3﷯﷮6﷯+ 𝑐1 𝑥﷮2﷯﷮2﷯+𝑐2𝑥+𝑐3 Again Integrating 𝑦= 𝑥﷮4﷯﷮24﷯+ 𝑐1 𝑥﷮3﷯﷮6﷯+ 𝑐2 𝑥﷮2﷯﷮2﷯+𝑐3𝑥+𝑐4 ∴ Number of Constants =4 Thus, Number of arbitrary Constants = Order of Differential Equation. ∴ Option D is correct

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