The solution of the differential equation (d y/d x)=(2 x y/x2-1-2 y) is

Question

The solution of the differential equation (d y/d x)=(2 x y/x2-1-2 y) is (A)  (x2/y)=(1/y)-2 ℓ n y+c (B) (x2/y2)=(1/y)-2 ℓ n y+c (C) x2 y= ln y+c (D) (x2/y)=2 ln y+c

Tardigrade Admin · Accepted Answer

(d y/d x)=(2 x y/x2-1-2 y) ⇒ x2 d y-(1+2 y) d y=2 x y d x or 2 x y d x-x2 d y=-(1+2 y) d y or (y d(x2)-x2 d y/y2)=-((1/y2)+(2/y)) d y d((x2/y))=-((1/y2)+(2/y)) d y Integrating (x2/y)=(1/y)-2 ℓ ny +c

Q. The solution of the differential equation $\frac{d y}{d x} = \frac{2 x y}{x ^{2} - 1 - 2 y}$ is

$\frac{x ^{2}}{y} = \frac{1}{y} - 2 ℓ n y + c$

$\frac{x ^{2}}{y ^{2}} = \frac{1}{y} - 2 ℓ n y + c$

$x^{2} y = ln y + c$

$\frac{x ^{2}}{y} = 2 ln y + c$

Q. The solution of the differential equation dxdy​=x2−1−2y2xy​ is

yx2​=y1​−2ℓny+c

y2x2​=y1​−2ℓny+c

x2y=lny+c

yx2​=2lny+c

dxdy​=x2−1−2y2xy​ ⇒x2dy−(1+2y)dy=2xydx or 2xydx−x2dy=−(1+2y)dy or y2yd(x2)−x2dy​=−(y21​+y2​)dy d(yx2​)=−(y21​+y2​)dy Integrating yx2​=y1​−2ℓ ny +c

Q. The solution of the differential equation $\frac{d y}{d x} = \frac{2 x y}{x ^{2} - 1 - 2 y}$ is

$\frac{x ^{2}}{y} = \frac{1}{y} - 2 ℓ n y + c$

$\frac{x ^{2}}{y ^{2}} = \frac{1}{y} - 2 ℓ n y + c$

$x^{2} y = ln y + c$

$\frac{x ^{2}}{y} = 2 ln y + c$