24y/x+ dy/dx =[f(xy)/f '(xy)]
IF=x
yx=∫x.[f(xy)/f '(xy)] dx
solve it now
1. y+x dy/dx = x [f(xy)/f '(xy)], thn f(xy)= ?
a) k(e)(x)2/2
b) k(e)(y)2/2
c) k(e)(xy)/2
d) k(e)(xy)
2. y= (c1 +c2)[sin(3x+c3)] - c4e(2x+c5)
Find the order of this differential equation:
a) 2
b) 3
c) 4
d) 5
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3 Answers
24
11finishing off with qsn 1...
y + x dydx = x f(xy) f'(xy)
yx + dydx = f(xy) f'(xy)
I.F. = e∫1x dx = x
so...
y + x dydx = x f(xy) f '(xy)
d(xy) = x f(xy) f '(xy) dx
∫ f '(xy) f (xy) d(xy) = ∫ x dx
ln (f(xy)) = x22 + ln k
or f(xy) = k ex2/2
so answer a...