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 ?