Ex 9.3, 3 - Chapter 9 Class 12 Differential Equations
Last updated at Dec. 16, 2024 by Teachoo
Variable separation - Equation given
Ex 9.3, 23 (MCQ)
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Chapter 9 Class 12 Differential Equations
Concept wise
- Order and Degree
- Gen and Particular Solution
- Formation of Differntial equation when general solution given
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Variable separation - Equation given
- Variable separation - Statement given
- Solving homogeneous differential equation
- Solving Linear differential equations - Equation given
- Solving Linear differential equations - Statement given
Transcript
Ex 9.3, 3 For each of the differential equations in Exercises 1 to 10, find the general solution : 𝑑𝑦/𝑑𝑥+𝑦=1(𝑦≠1) 𝑑𝑦/𝑑𝑥+𝑦=1 𝑑𝑦/𝑑𝑥=1−𝑦 𝑑𝑦 = (1 − y) dx 𝑑𝑦/(1 − 𝑦) = dx 𝒅𝒚/(𝒚 − 𝟏) = −dx Integrating both sides. ∫1▒〖𝑑𝑦/(𝑦 − 1)=〗 ∫1▒〖−𝑑𝑥〗 log (y − 1) = −x + C y − 1 = e(−x + C) y − 1 = e−x × eC y = e−x × eC + 1 Putting eC = A y = Ae−x + 1 is the general solution
