The solution of the differential equation y (2x4+y)(dy/dx)=(1-4xy2)x2 is given by

Question

The solution of the differential equation y (2x4+y)(dy/dx)=(1-4xy2)x2 is given by (A) 3(x2y)2+y3-x3=c (B) xy2+(y3/3)-(x3/3)+c=0 (C) (2/5)yx5+(y3/3)=(x3/3)-(4xy3/3)+c (D) None of these

Tardigrade Admin · Accepted Answer

y (2x4+y)(dy/dx)=(1-4xy2)x2 or 2x4y dy+y2 dy+4x3y2dx-x2 dx=0 or 2x2y (x2 dy +2xy dx)+y2 dy-x2 dx=0 or 2x2 y d(x2y)+y2 dy-x2 dx=0 Integrating, we get (x2y)2+(y3/3)-(x3/3)=c or 3(x2y)2+y3-x3=c

Q. The solution of the differential equation $y (2 x^{4} + y) \frac{d y}{d x} = (1 - 4 x y^{2}) x^{2}$ is given by

$3 (x^{2} y)^{2} + y^{3} - x^{3} = c$

$x y^{2} + \frac{y ^{3}}{3} - \frac{x ^{3}}{3} + c = 0$

$\frac{2}{5} y x^{5} + \frac{y ^{3}}{3} = \frac{x ^{3}}{3} - \frac{4 x y ^{3}}{3} + c$

None of these

Q. The solution of the differential equation y(2x4+y)dxdy​=(1−4xy2)x2 is given by

3(x2y)2+y3−x3=c

xy2+3y3​−3x3​+c=0

52​yx5+3y3​=3x3​−34xy3​+c

None of these

y(2x4+y)dxdy​=(1−4xy2)x2 or 2x4ydy+y2dy+4x3y2dx−x2dx=0 or 2x2y(x2dy+2xydx)+y2dy−x2dx=0 or 2x2yd(x2y)+y2dy−x2dx=0 Integrating, we get (x2y)2+3y3​−3x3​=c or 3(x2y)2+y3−x3=c

Q. The solution of the differential equation $y (2 x^{4} + y) \frac{d y}{d x} = (1 - 4 x y^{2}) x^{2}$ is given by

$3 (x^{2} y)^{2} + y^{3} - x^{3} = c$

$x y^{2} + \frac{y ^{3}}{3} - \frac{x ^{3}}{3} + c = 0$

$\frac{2}{5} y x^{5} + \frac{y ^{3}}{3} = \frac{x ^{3}}{3} - \frac{4 x y ^{3}}{3} + c$