Check sibling questions

Example 26 - Find particular solution log (dy/dx) =3x + 4y

Example 26 - Chapter 9 Class 12 Differential Equations - Part 2
Example 26 - Chapter 9 Class 12 Differential Equations - Part 3


Transcript

Example 26 Find the particular solution of the differential equation log(𝑑𝑦/𝑑π‘₯)=3π‘₯+4𝑦 given that 𝑦=0 π‘€β„Žπ‘’π‘› π‘₯=0 log(𝑑𝑦/𝑑π‘₯)=3π‘₯+4𝑦 𝑑𝑦/𝑑π‘₯ = e(3x + 4y) 𝑑𝑦/𝑑π‘₯ = e3x e4y Separating the variables 𝑑𝑦/𝑒^4𝑦 = e3x dx eβˆ’4y dy = e3x dx Integrating both sides ∫1▒〖𝑒^(βˆ’4𝑦) 𝑑𝑦〗=∫1▒𝑒^3π‘₯ 𝑑π‘₯ 𝑒^(βˆ’4𝑦)/(βˆ’4)=𝑒^3π‘₯/3+𝐢 0=𝑒^3π‘₯/3+𝑒^(βˆ’4𝑦)/4+𝐢 𝑒^3π‘₯/3 + 𝑒^(βˆ’4𝑦)/4 + C = 0 (4𝑒3π‘₯" + " 3𝑒^(βˆ’4𝑦))/12 + C = 0 (4𝑒3π‘₯" + " 3𝑒^(βˆ’4𝑦) + 12𝐢)/12 " = 0" 4𝑒^3π‘₯ + 3𝑒^(βˆ’4𝑦) + 12C = 0 Given y = 0 when x = 0 …(1) Putting x = 0 & y = 0 in (1) 4𝑒^(3(0)) + 3𝑒^(βˆ’4(0)) + 12C = 0 4𝑒^0 + 3𝑒^0 + 12C = 0 4 + 3 + 12C = 0 7 + 12C = 0 12C = – 7 C = (βˆ’7)/12 Putting value of C in (1) 4𝑒^3π‘₯ + 3𝑒^(βˆ’4𝑦) + 12C = 0 4𝑒^3π‘₯ + 3𝑒^(βˆ’4𝑦) + 12((βˆ’7)/12) = 0 πŸ’π’†^πŸ‘π’™ + πŸ‘π’†^(βˆ’πŸ’π’š) βˆ’ 7 = 0

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.