Ex 9.5, 12 - Chapter 9 Class 12 Differential Equations
Last updated at April 16, 2024 by Teachoo
Ex 9.5
Ex 9.5, 2
Ex 9.5, 3 Important
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Ex 9.5, 5 Important
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Ex 9.5, 7 Important
Ex 9.5, 8 Important
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Ex 9.5, 12 Important You are here
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 April 16, 2024 by Teachoo
Ex 9.5, 12 For each of the differential equation find the general solution : (𝑥+3𝑦^2 ) 𝑑𝑦/𝑑𝑥=𝑦(𝑦>0) Step 1 : Put In form 𝑑𝑦/𝑑𝑥 + py = Q or 𝑑𝑥/𝑑𝑦 + P1x = Q1 (𝑥+3𝑦^2 ) 𝑑𝑦/𝑑𝑥=𝑦 𝑑𝑦/𝑑𝑥 = 𝑦/(𝑥+3𝑦^2 ) This is not of the form 𝑑𝑦/𝑑𝑥 + Py = Q ∴ We need to find 𝒅𝒙/𝒅𝒚 𝑑𝑥/𝑑𝑦 = (𝑥 + 3𝑦^2)/𝑦 𝒅𝒙/𝒅𝒚 = 𝒙/𝒚 + (𝟑𝒚^𝟐)/𝒚 Step 2 : Find P1 and Q1 Comparing with 𝑑𝑦/𝑑𝑥 + P1x = Q1 where P1 = (−𝟏)/𝒚 & Q1 = 3y Step 3 : Finding Integrating factor IF = 𝒆^(∫1▒𝒑_𝟏 𝒅𝒚) IF = 𝑒^(∫1▒(−1)/𝑦 𝑑𝑦" " ) IF = e−log y IF = 𝑒^log〖𝑦^(−1) 〗 IF = y−1 IF = 𝟏/𝒚 Step 4 : Solution of the equation Solution is x(IF) = ∫1▒〖(𝑄1×𝐼𝐹)𝑑𝑦+𝐶〗 x(1/𝑦)=∫1▒〖3𝑦×1/𝑦 𝑑𝑦+𝐶〗 𝑥/𝑦 = 3∫1▒〖𝑑𝑦+𝐶〗 𝑥/𝑦 = 3𝑦+𝐶 𝒙 = 𝟑𝒚^𝟐+𝑪y