Ex 9.3, 11 - Which differential equations has y = c1 ex + c2 e-x - Ex 9.3

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  1. Chapter 9 Class 12 Differential Equations
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Ex 9.3, 11 Which of the following differential equations has 𝑦=𝑐1 𝑒﷮𝑥﷯+𝑐2 𝑒﷮−𝑥﷯ as the general solution ? (A) 𝑑﷮2﷯𝑦﷮𝑑 𝑥﷮2﷯﷯+𝑦=0 (B) 𝑑﷮2﷯𝑦﷮𝑑 𝑥﷮2﷯﷯−𝑦=0 (C) 𝑑﷮2﷯𝑦﷮𝑑 𝑥﷮2﷯﷯+1=0 (D) 𝑑﷮2﷯𝑦﷮𝑑 𝑥﷮2﷯﷯−𝑦=0 𝑦=𝑐1 𝑒﷮𝑥﷯+𝑐2 𝑒﷮−𝑥﷯ ∴ Differentiating Both Sides w.r.t. 𝑥 𝑑𝑦﷮𝑑𝑥﷯=𝑐1 𝑒﷮𝑥﷯+𝑐2 𝑒﷮−𝑥﷯ Again differentiating both sides w.r.t.x 𝑑﷮2﷯𝑦﷮𝑑 𝑥﷮2﷯﷯=𝑐1 𝑒﷮𝑥﷯−𝑐2 𝑒﷮−𝑥﷯ −1﷯ 𝑑﷮2﷯𝑦﷮𝑑 𝑥﷮2﷯﷯=𝑐1 𝑒﷮𝑥﷯+𝑐2 𝑒﷮−𝑥﷯ 𝑑﷮2﷯𝑦﷮𝑑 𝑥﷮2﷯﷯=𝑦 𝑑﷮2﷯𝑦﷮𝑑 𝑥﷮2﷯﷯ −𝑦=0 ∴ Option B is correct

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