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Question 1 Form a differential equation representing the given family of curves by eliminating arbitrary constants π‘Ž and 𝑏. π‘₯/π‘Ž+𝑦/𝑏=1 Here , we eliminate constants by Differentiating both sides w.r.t.x Now, π‘₯/π‘Ž+𝑦/𝑏=1 Differentiating Both Sides w.r.t. π‘₯ 1/π‘Ž+1/𝑏.𝑑𝑦/𝑑π‘₯=0 1/𝑏.𝑑𝑦/𝑑π‘₯=(βˆ’1)/( π‘Ž) The number of times we differentiate is equal to number of constants π’…π’š/𝒅𝒙=(βˆ’π’ƒ)/( 𝒂) Again Differentiating Both Sides w.r.t. π‘₯ (𝒅^𝟐 π’š)/(𝒅𝒙^𝟐 )=𝟎 Thus, Differential Equation Is :- π’š^β€²β€²=𝟎

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.