Examples
Example 1 (ii) Important
Example 1 (iii) Important
Example 2
Example 3 Important
Example 4 Deleted for CBSE Board 2022 Exams
Example 5 Deleted for CBSE Board 2022 Exams
Example 6 Important Deleted for CBSE Board 2022 Exams
Example 7 Deleted for CBSE Board 2022 Exams
Example 8 Deleted for CBSE Board 2022 Exams
Example 9
Example 10
Example 11
Example 12 Important
Example 13
Example 14 Important
Example 15 Important
Example 16
Example 17 Important
Example 18 Important
Example 19
Example 20 Important
Example 21 Deleted for CBSE Board 2022 Exams
Example 22 Important
Example 23 Important
Example 24
Example 25 Deleted for CBSE Board 2022 Exams
Example 26 You are here
Example 27 Important
Example 28 Important Deleted for CBSE Board 2022 Exams
Last updated at Dec. 11, 2019 by Teachoo
Example 26 Find the particular solution of the differential equation log(ππ¦/ππ₯)=3π₯+4π¦ given that π¦=0 π€βππ π₯=0 log(ππ¦/ππ₯)=3π₯+4π¦ ππ¦/ππ₯ = e(3x + 4y) ππ¦/ππ₯ = e3x e4y Separating the variables ππ¦/π^4π¦ = e3x dx eβ4y dy = e3x dx Integrating both sides β«1βγπ^(β4π¦) ππ¦γ=β«1βπ^3π₯ ππ₯ π^(β4π¦)/(β4)=π^3π₯/3+πΆ 0=π^3π₯/3+π^(β4π¦)/4+πΆ π^3π₯/3 + π^(β4π¦)/4 + C = 0 (4π3π₯" + " 3π^(β4π¦))/12 + C = 0 (4π3π₯" + " 3π^(β4π¦) + 12πΆ)/12 " = 0" 4π^3π₯ + 3π^(β4π¦) + 12C = 0 Given y = 0 when x = 0 β¦(1) Putting x = 0 & y = 0 in (1) 4π^(3(0)) + 3π^(β4(0)) + 12C = 0 4π^0 + 3π^0 + 12C = 0 4 + 3 + 12C = 0 7 + 12C = 0 12C = β 7 C = (β7)/12 Putting value of C in (1) 4π^3π₯ + 3π^(β4π¦) + 12C = 0 4π^3π₯ + 3π^(β4π¦) + 12((β7)/12) = 0 ππ^ππ + ππ^(βππ) β 7 = 0
