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Last updated at Dec. 10, 2019 by Teachoo
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Ex 9.3, 3 Form a differential equation representing the given family of curves by eliminating arbitrary constants ๐ and ๐. ๐ฆ=๐ ๐^3๐ฅ+๐ ๐^(โ2๐ฅ) Since it has two variables, we will differentiate twice ๐ฆ=๐ ๐^3๐ฅ+๐ ๐^(โ2๐ฅ) โด Differentiating Both Sides w.r.t. ๐ฅ ๐๐ฆ/๐๐ฅ=๐/๐๐ฅ [๐๐^3๐ฅ+๐ ๐^(โ2๐ฅ) ] =๐๐^3๐ฅร3+๐ ๐^(โ2๐ฅ)ร(โ2) =3๐๐^3๐ฅโ2๐ ๐^(โ2๐ฅ) โด ๐ฆ^โฒ=3๐๐^3๐ฅโ2๐ ๐^(โ2๐ฅ) ...(1) ๐ฆ^โฒ=3๐๐^3๐ฅโ2๐ ๐^(โ2๐ฅ) Again differentiating w.r.t. ๐ฅ ๐ฆ^โฒโฒ=๐/๐๐ฅ [3๐๐^3๐ฅโ2๐ ๐^(โ2๐ฅ) ] ๐ฆ^โฒโฒ=3๐๐^3๐ฅ (3)โ2๐ ๐^(โ2๐ฅ) (โ2) โด ๐ฆ^โฒโฒ=9๐๐^3๐ฅ+4๐ ๐^(โ2๐ฅ) Subtracting (2) From (1) ๐ฆ^โฒโฒโ๐ฆ^โฒ=9๐๐^3๐ฅ+4๐ ๐^(โ2๐ฅ)โ3๐๐^3๐ฅ+2๐ ๐^(โ2๐ฅ) ๐ฆ^โฒโฒโ๐ฆ^โฒ=6๐๐^3๐ฅ+6๐ ๐^(โ2๐ฅ) ๐ฆ^โฒโฒโ๐ฆ^โฒ=6(๐๐^3๐ฅ+๐๐^(โ2๐ฅ)) ๐ฆ^โฒโฒโ๐ฆ^โฒ=6y ๐^โฒโฒโ๐^โฒโ๐๐=๐ is the required differential equation. (As y = ๐^3๐ฅ + b๐^3๐ฅ)
Ex 9.3
Ex 9.3, 2 Not in Syllabus - CBSE Exams 2021
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Ex 9.3, 4 Not in Syllabus - CBSE Exams 2021
Ex 9.3, 5 Important Not in Syllabus - CBSE Exams 2021
Ex 9.3, 6 Not in Syllabus - CBSE Exams 2021
Ex 9.3, 7 Important Not in Syllabus - CBSE Exams 2021
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Ex 9.3, 9 Not in Syllabus - CBSE Exams 2021
Ex 9.3, 10 Important Not in Syllabus - CBSE Exams 2021
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