Differential EquationHard
Question
he solution of the differential equation y1 y3 = 3y22 is
Options
A.x = A1y2 + A2 y + A3
B.x = A1 y + A2
C.x = A1 y2 + A2 y
D.none of these
Solution
y1y3 = 3y22
⇒ ln y2 = 3ln y1 + ln c
y2 = cy13
= cy1
-
= cy + c2
= - cy - c2
x = -
- c2y + c3
∴ x = A1y2 + A2y + A3
⇒ ln y2 = 3ln y1 + ln cy2 = cy13
= cy1-
= cy + c2 = - cy - c2x = -
- c2y + c3∴ x = A1y2 + A2y + A3
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