# Ex 9.3, 3 - Chapter 9 Class 12 Differential Equations (Term 2)

Last updated at Dec. 10, 2019 by Teachoo

Ex 9.3

Ex 9.3, 1
Deleted for CBSE Board 2023 Exams

Ex 9.3, 2 Deleted for CBSE Board 2023 Exams

Ex 9.3, 3 Important Deleted for CBSE Board 2023 Exams You are here

Ex 9.3, 4 Deleted for CBSE Board 2023 Exams

Ex 9.3, 5 Important Deleted for CBSE Board 2023 Exams

Ex 9.3, 6 Deleted for CBSE Board 2023 Exams

Ex 9.3, 7 Important Deleted for CBSE Board 2023 Exams

Ex 9.3, 8 Deleted for CBSE Board 2023 Exams

Ex 9.3, 9 Deleted for CBSE Board 2023 Exams

Ex 9.3, 10 Important Deleted for CBSE Board 2023 Exams

Ex 9.3, 11 (MCQ) Deleted for CBSE Board 2023 Exams

Ex 9.3, 12 (MCQ) Important Deleted for CBSE Board 2023 Exams

Chapter 9 Class 12 Differential Equations

Serial order wise

Last updated at Dec. 10, 2019 by Teachoo

Ex 9.3, 3 Form a differential equation representing the given family of curves by eliminating arbitrary constants 𝑎 and 𝑏. 𝑦=𝑎 𝑒^3𝑥+𝑏 𝑒^(−2𝑥) Since it has two variables, we will differentiate twice 𝑦=𝑎 𝑒^3𝑥+𝑏 𝑒^(−2𝑥) ∴ Differentiating Both Sides w.r.t. 𝑥 𝑑𝑦/𝑑𝑥=𝑑/𝑑𝑥 [𝑎𝑒^3𝑥+𝑏 𝑒^(−2𝑥) ] =𝑎𝑒^3𝑥×3+𝑏 𝑒^(−2𝑥)×(−2) =3𝑎𝑒^3𝑥−2𝑏 𝑒^(−2𝑥) ∴ 𝑦^′=3𝑎𝑒^3𝑥−2𝑏 𝑒^(−2𝑥) ...(1) 𝑦^′=3𝑎𝑒^3𝑥−2𝑏 𝑒^(−2𝑥) Again differentiating w.r.t. 𝑥 𝑦^′′=𝑑/𝑑𝑥 [3𝑎𝑒^3𝑥−2𝑏 𝑒^(−2𝑥) ] 𝑦^′′=3𝑎𝑒^3𝑥 (3)−2𝑏 𝑒^(−2𝑥) (−2) ∴ 𝑦^′′=9𝑎𝑒^3𝑥+4𝑏 𝑒^(−2𝑥) Subtracting (2) From (1) 𝑦^′′−𝑦^′=9𝑎𝑒^3𝑥+4𝑏 𝑒^(−2𝑥)−3𝑎𝑒^3𝑥+2𝑏 𝑒^(−2𝑥) 𝑦^′′−𝑦^′=6𝑎𝑒^3𝑥+6𝑏 𝑒^(−2𝑥) 𝑦^′′−𝑦^′=6(𝑎𝑒^3𝑥+𝑏𝑒^(−2𝑥)) 𝑦^′′−𝑦^′=6y 𝒚^′′−𝒚^′−𝟔𝒚=𝟎 is the required differential equation. (As y = 𝑎^3𝑥 + b𝑒^3𝑥)