Find the solution of 2 x-3y-1 dy-dx- 4x-2y-1-

The correct option is A 2xy+2y 3y^2 x 2x^2= k. 2 ( x 3y+1 )dy/dx= 4x 2y+1. 2 ( x 3y+1 )dy= (4x 2y+1)dx 2 ( xdy+ydx )+2 ( 1 3y )dy ( 1+ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Variable Separable Method

Find the solu...

Question

Find the solution of $2 (x - 3 y + 1) \frac{d y}{d x} = 4 x - 2 y + 1.$

2 x y + 2 y - 3 y^{2} - x - 2 x^{2} = k .

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

2 x y - 2 y - 3 y^{2} - x - 2 x^{2} = k .

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 x y - 2 y + 3 y^{2} - x - 2 x^{2} = k .

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 x y + 2 y + 3 y^{2} - x - 2 x^{2} = k .

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $2 x y + 2 y - 3 y^{2} - x - 2 x^{2} = k .$
$2 (x - 3 y + 1) \frac{d y}{d x} = 4 x - 2 y + 1.$
$2 (x - 3 y + 1) d y = (4 x - 2 y + 1) d x$
$2 (x d y + y d x) + 2 (1 - 3 y) d y - (1 + 4 x) d x = 0$
$2 d x y + 2 (1 - 3 y) d y - (1 + 4 x) d x = 0$
Integrating we get,
$2 x y + 2 (y - \frac{3 y^{2}}{2}) - (x + 2 x^{2}) = c$
or $2 x y + 2 y - 3 y^{2} - x - 2 x^{2} = k .$

Suggest Corrections

Similar questions

Q. Find the value of

k

, if the lines joining to the points of inter section of the curve

2 x^{2} - 2 x y + 3 y^{2} + 2 x - y - 1 = 0

and the line

x + 2 y = k

are mutually perpendicular.

Q. The lines joining the joining the origin to the points of intersection of

x + 2 y = k

with the pair of lines

2 x^{2} - 2 x y + 3 y^{2} + 2 x - y - 1 = 0

are at right angles then k=

The equation of directrix of a conic is
$L : x + y - 1 = 0$ and the focus is the point $(0, 0)$ . Find the equation of the conic if its eccentricity is
$\frac{1}{\sqrt{2}}$

Minimum value of $x^{2} + 2 x y + 3 y^{2} - 6 x - 2 y$ $x, y, ϵ R$ is

Q. Obtain real solutions of simultaneous equations.

x y + 3 y^{2} - x + 4 y - 7 = 0

2 x y + y^{2} - 2 x - 2 y + 1 = 0

Join BYJU'S Learning Program

Find the solution of 2(x−3y+1)dydx=4x−2y+1.

The correct option is A 2xy+2y−3y2−x−2x2=k.2(x−3y+1)dydx=4x−2y+1.2(x−3y+1)dy=(4x−2y+1)dx2(xdy+ydx)+2(1−3y)dy−(1+4x)dx=02dxy+2(1−3y)dy−(1+4x)dx=0Integrating we get,2xy+2(y−3y22)−(x+2x2)=c or 2xy+2y−3y2−x−2x2=k.

Find the solution of $2 (x - 3 y + 1) \frac{d y}{d x} = 4 x - 2 y + 1.$