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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.