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Ex 9.5
Ex 9.5, 2
Ex 9.5, 3 Important
Ex 9.5, 4
Ex 9.5, 5 Important
Ex 9.5, 6
Ex 9.5, 7 Important
Ex 9.5, 8 Important
Ex 9.5, 9
Ex 9.5, 10
Ex 9.5, 11 You are here
Ex 9.5, 12 Important
Ex 9.5, 13
Ex 9.5, 14 Important
Ex 9.5, 15
Ex 9.5, 16 Important
Ex 9.5, 17 Important
Ex 9.5, 18 (MCQ)
Ex 9.5, 19 (MCQ) Important
Last updated at Aug. 14, 2023 by Teachoo
Ex 9.5, 11 For each of the differential equation find the general solution : 𝑦 𝑑𝑥+(𝑥−𝑦^2 )𝑑𝑦=0 Step 1 : Put in form 𝑑𝑦/𝑑𝑥 + Py = Q or 𝑑𝑥/𝑑𝑦 + P1 x = Q1, y dx + (x − y2) dy = 0 y dx = − (x − y2)dy 𝑑𝑦/𝑑𝑥 = (−𝑦)/(𝑥−𝑦^2 ) This is not of the form 𝑑𝑦/𝑑𝑥 + Py = Q ∴ We find 𝒅𝒙/𝒅𝒚 𝑑𝑥/𝑑𝑦 = (𝑦^2 − 𝑥)/𝑦 𝑑𝑥/𝑑𝑦 = y − 𝑥/𝑦 𝒅𝒙/𝒅𝒚 + 𝒙/𝒚 = y Step 2 : Find P1 and Q1 Comparing (1) with 𝑑𝑥/𝑑𝑦 + P1 x = Q1 Where P1 = 𝟏/𝒚 & Q1 = y Step 3 : Find Integrating factor, IF = 𝒆^∫1▒〖𝒑𝟏 𝒅𝒚〗 = 𝑒^∫1▒𝑑𝑦/𝑦 = 𝑒^log𝑦 = y Step 4 : Solution of the equation Solution is x (IF) = ∫1▒〖(𝑄1×𝐼𝐹)𝑑𝑦+𝑐〗 xy = ∫1▒〖𝒚×𝒚 𝒅𝒚+𝒄〗 xy = ∫1▒〖𝑦^2 𝑑𝑦+𝑐〗 xy = 𝑦^3/3+𝐶 x = 𝑦^3/3𝑦+𝐶/𝑦 x = 𝒚^𝟐/𝟑+𝑪/𝒚