Example 15 - Chapter 9 Class 12 Differential Equations
Last updated at Dec. 16, 2024 by Teachoo
Examples
Example 1 (i)
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Chapter 9 Class 12 Differential Equations
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Transcript
Example 15 Find the general solution of the differential equation π₯ ππ¦/ππ₯+2π¦=π₯^2 (π₯β 0) π₯ ππ¦/ππ₯+2π¦=π₯^2 (π₯ ππ¦)/(π₯ ππ₯) + 2π¦/π₯ = π₯^2/π₯ Dividing both sides by x π π/π π + ππ/π = x Differential equation is of the form ππ¦/ππ₯+ππ¦=π where P = 2/π₯ & Q = x Finding Integrating Factor IF = π^β«1βγπ ππ₯γ IF = π^β«1βγπ/π π πγ IF = π^(2 logβ‘π₯ ) IF = π^(γlogβ‘π₯γ^2 ) I.F = x2 Solution of differential equation is y Γ IF = β«1βγ(πΈΓππ )π π+πγ yx2 = β«1βγπ₯Γπ₯^2 ππ₯+πγ yx2 = β«1βγπ^π π π+πγ x2 y = π₯^4/4+π y = π^π/π+ππ^(βπ) is the required general solution
