Ex 9.2, 1 - Verify given functions is a solution of - Chapter 9 - Gen and Particular Solution

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  1. Chapter 9 Class 12 Differential Equations
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Ex 9.2, 1 Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation : ๐‘ฆ=๐‘’^๐‘ฅ+1 : ๐‘ฆ^โ€ฒโ€ฒโˆ’๐‘ฆ^โ€ฒ=0 ๐‘ฆ=๐‘’^๐‘ฅ+1 ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=๐‘‘/๐‘‘๐‘ฅ (๐‘’^๐‘ฅ+1) =๐‘’^๐‘ฅ (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 )=๐‘‘/๐‘‘๐‘ฅ (๐‘‘๐‘ฆ/๐‘‘๐‘ฅ) = ๐‘’^๐‘ฅ Now, we have to verify ๐‘ฆ^โ€ฒโ€ฒโˆ’๐‘ฆ^โ€ฒ=0 Taking L.H.S ๐‘ฆ^โ€ฒโ€ฒโˆ’๐‘ฆ^โ€ฒ =๐‘’^๐‘ฅโˆ’๐‘’^๐‘ฅ =0 = R.H.S Hence verified.

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