Misc 17 - Chapter 9 Class 12 Differential Equations

Transcript

Misc 17 The general solution of a differential equation equation of the type 𝑑𝑥﷮𝑑𝑦﷯+P1𝑥=𝑄1 is (A) 𝑦 𝑒﷮ ﷮﷮P1 𝑑𝑦﷯﷯= ﷮﷮ 𝑄1 𝑒﷮ ﷮﷮P1 𝑑𝑦﷯﷯﷯𝑑𝑦+𝐶﷯ (B) 𝑦. 𝑒﷮ ﷮﷮P1 𝑑𝑥﷯﷯= ﷮﷮ 𝑄1 𝑒﷮ ﷮﷮P1 𝑑𝑥﷯﷯﷯𝑑𝑥+𝐶﷯ (C) 𝑥 𝑒﷮ ﷮﷮P1 𝑑𝑦﷯﷯= ﷮﷮ 𝑄1 𝑒﷮ ﷮﷮P1 𝑑𝑦﷯﷯﷯𝑑𝑦+𝐶﷯ (D) 𝑥 𝑒﷮ ﷮﷮P1 𝑑𝑥﷯﷯= ﷮﷮ 𝑄1 𝑒﷮ ﷮﷮P1 𝑑𝑥﷯﷯﷯𝑑𝑥+𝐶﷯ Differential equation is of type 𝑑𝑥﷮𝑑𝑦﷯+P1𝑥=𝑄1 where P1 & Q1 are functions of y IF = 𝑒﷮ ﷮﷮P1 𝑑𝑦﷯﷯ General solution is x (IF) = ﷮﷮ 𝑄1×𝐼𝐹﷯𝑑𝑦+𝑐﷯ 𝑥 𝑒﷮ ﷮﷮P1 𝑑𝑦﷯﷯= ﷮﷮ 𝑄1 𝑒﷮ ﷮﷮P1 𝑑𝑦﷯﷯﷯𝑑𝑦+𝐶﷯ Option (C) is the correct answer.