Ex 9.5

Chapter 9 Class 12 Differential Equations
Serial order wise

### Transcript

Ex 9.5, 11 For each of the differential equation find the general solution : π¦ ππ₯+(π₯βπ¦^2 )ππ¦=0 Step 1 : Put in form ππ¦/ππ₯ + Py = Q or ππ₯/ππ¦ + P1 x = Q1, y dx + (x β y2) dy = 0 y dx = β (x β y2)dy ππ¦/ππ₯ = (βπ¦)/(π₯βπ¦^2 ) This is not of the form ππ¦/ππ₯ + Py = Q β΄ We find ππ/ππ ππ₯/ππ¦ = (π¦^2 β π₯)/π¦ ππ₯/ππ¦ = y β π₯/π¦ ππ/ππ + π/π = y Step 2 : Find P1 and Q1 Comparing (1) with ππ₯/ππ¦ + P1 x = Q1 Where P1 = π/π & Q1 = y Step 3 : Find Integrating factor, IF = π^β«1βγππ ππγ = π^β«1βππ¦/π¦ = π^logβ‘π¦ = y Step 4 : Solution of the equation Solution is x (IF) = β«1βγ(π1ΓπΌπΉ)ππ¦+πγ xy = β«1βγπΓπ ππ+πγ xy = β«1βγπ¦^2 ππ¦+πγ xy = π¦^3/3+πΆ x = π¦^3/3π¦+πΆ/π¦ x = π^π/π+πͺ/π