Question

Let αx =exp(x βyγ) be the solution of the differential equation 2 x 2 ydy −(1− xy 2) dx = 0, x >0 , y(2)=$\sqrt {log_e^2}$​. Then α +β − γ equals :

• A. 0
• B. $-1$
• C. 1
• D. 3

Answer 1

Answer: (C)

1

Answer 2

αx=exβ⋅y7
2x2ydxdy​=1−x⋅y2y2=t
x2dxdt​=1−xt
dxdt​+xt​=x21​ I.F. =e(nx=x
t(x)=∫x21​⋅xdx
y2⋅x=ℓnx+C
∴2⋅ln2=ℓn2+C
∴C=ln2
Hence, xy2=ℓn2x
∴2x=ex⋅y2
Hence α=2,β=1,γ=2