Ex 9.5

Chapter 9 Class 12 Differential Equations
Serial order wise

### Transcript

Ex 9.5, 12 For each of the differential equation find the general solution : (π₯+3π¦^2 ) ππ¦/ππ₯=π¦(π¦>0) Step 1 : Put In form ππ¦/ππ₯ + py = Q or ππ₯/ππ¦ + P1x = Q1 (π₯+3π¦^2 ) ππ¦/ππ₯=π¦ ππ¦/ππ₯ = π¦/(π₯+3π¦^2 ) This is not of the form ππ¦/ππ₯ + Py = Q β΄ We need to find ππ/ππ ππ₯/ππ¦ = (π₯ + 3π¦^2)/π¦ ππ/ππ = π/π + (ππ^π)/π Step 2 : Find P1 and Q1 Comparing with ππ¦/ππ₯ + P1x = Q1 where P1 = (βπ)/π & Q1 = 3y Step 3 : Finding Integrating factor IF = π^(β«1βπ_π ππ) IF = π^(β«1β(β1)/π¦ ππ¦" " ) IF = eβlog y IF = π^logβ‘γπ¦^(β1) γ IF = yβ1 IF = π/π Step 4 : Solution of the equation Solution is x(IF) = β«1βγ(π1ΓπΌπΉ)ππ¦+πΆγ x(1/π¦)=β«1βγ3π¦Γ1/π¦ ππ¦+πΆγ π₯/π¦ = 3β«1βγππ¦+πΆγ π₯/π¦ = 3π¦+πΆ π = ππ^π+πͺy