(1+x²+y²+x²y²) ^1/2 + xy dy/dx =0 how to solve dis diffrential equation!?! ..please ans asap!! :)

1. Solve diff eqn   dy/dx  +  y cotx  =  x2 cotx  +  2x
2. Find distance of the point (-2 , 3 , -4 )  from the line  x + 2/3 = 2y +3/4 = 3z + 4/5  m,easutres II to plane   4x + 12y - 3z +1 =0

how can we solve ; dy/dx=tan 2(x+y) or dy/dx=tan square (x+y)

number chart for maths fair

Solve (1+y²)dx = (tan^-1y - x)dy

if x=a(t+sint) , y=a(1-cost) , show that y''=1/a , at t=90deegre .(or) pi/2

dy/dx+xsin2y=x³cos²y

Solve the differential equation:

x dy/dx + y = x cosx + sinx

given that y(pie/2) =1.

form the differential equation of a family of circles touching y- axis at origin

Solve:

dy/dx = 1 + x + y + xy

Answer given in the book is : log | 1 + y| = x + 1/2 x² + C

solve-

(x² + xy)dy = ( x² + y²)dx

Solve:

( 1 + e^x/y )dx + e^x/y ( 1 - x/y) dy = 0

The answer given in the book is : x + y e^x/y = C₁

Show that Ax² + By²=1 is a solution of the differential equation  x[y( d²y/dx²) + (dy/dx)²] = y dy/dx.

Solve:

x ( 1 + y²) dx - y ( 1 + x² ) dy = 0, given that y = 0 when x = 1

The answer given in the book is : ( 1 + x² ) = 2 ( 1 + y² )

Solve the differential equation: (tan^-1y- x)dy=(1+y^2)dx

Solve:

cos x cos y dy + sin x sin y dx= 0

The answer give in the book is : sin y = C cos x

Q10.   (x-y) dy/dx =x + 2y

Form the differential equation of the family of circles having centre on y-axis and radius 3 units...... see in this question in ncert values of arbitaray constant is calculated and then put in the given eqn ..... but can it be also done if we jst differentiate the given eqn . because in that also nothing much is changed except the answer !.

can the form can have one or more forms ?

sec²x tany dx +sec²y tanx dy=0. Form the differential eqation. plz help me

form the differential equation of the family of circles touching the second quadrant

solve differential equation sqrt 1+x²+y²+x²y² + xy dy/dx=0

y=sin(log x)prove that

x² d²y/dx² +dy/dx +y =0

x.dy/dx=y(log y-log x - 1)

 find the differential equation of all the parabolas with latus rectum 4a and whose axes r parallel to x-axis.

solve the differential equation-

x² dy/dx= 2xy+y²

Q1  Verify that y2 =4ax is a solution of the differential equation y= x dy/dx + a dx/dy

  Assume that a rain drop evaporates at a rate proportional to its surface . form a differrential equation involving the rate of change of the radius of the rain drop....

ques. To solve the differential equation : y - x.dy/dx=a( y²  + x².dy/dx) ; y(a)=a.

Solve:

( e^y + 1) cosx dx + e^y sin x dy = 0

The answer given in the book is : ( 1 + e^y ) sin x = C₁