Questions
If y1 and y2 are two solution to the differential equation and then k =
a
y1+2y2
b
y1−2y2
c
y1−y2
d
2y1y2
detailed solution
Correct option is C
y1y2 are two solution of dydx+p(x)y=Q(x)→(1) Then dy1dx+p(x)y1=Q(x)→(2) And dy2dx+p(x)y2=Q(x)→(3)Eq (1)-Eq(2)⇒dy−y1dx+p(x)y−y1=0→(4) Eq (2)-Eq(3)⇒dy1−y2dx+p(x)y1−y2=0→(5)Eq (4)Eq(5)⇒ddxy1−y2ddxy1−y2=y−y1y1−y2∫ddxy−y1y−y1=∫ddxy1−y2y1−y2⇒lny−y1=lny1−y2+lnc⇒y−y1=cy1−y2⇒y=y1+cy1−y2Talk to our academic expert!
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