#Stay_Ahead of your Class

Listen NCERT Audio Books to boost your productivity and retention power by 2X.

In each of the following differential equation show that it is homogeneous and solve it.

xdy = (x + y)dx

(x^{2} - y^{2})dx + 2xydy = 0

x^{2}dy + y(x + y)dx = 0

(x - y)dy - (x + y)dx = 0

(x + y)dy + (y - 2x)dx = 0

(x^{2} + 3xy + y^{2})dx - x^{2}dy = 0

2xydx + (x^{2} + 2y^{2})dy = 0

x^{2} = x^{2} + xy + y^{2}

(x - y) = x + 3y

(x^{3} + 3xy^{2})dx + (y^{3} + 3x^{2}y)dy = 0

dy = ydx

x^{2} + y^{2} = xy

(log y - log x + 1)

x–y + xsin = 0

x = y - xcos^{2}

Find the particular solution of the different equation.2xy + y^{2} - 2x^{2} = 0, it being given that y = 2 when x = 1

Find the particular solution of the differential equation dx + xdy = 0, it being given that y = when x = 1.

Find the particular solution of the differential equation given that y = 1 when x = 1.

Find the particular solution of the differential equation xe^{y/x} - y + x = 0, given that y(1) = 0.

Find the particular solution of the differential equation xe^{y/x} - y + x = 0, given that y(e) = 0.

The slope of the tangent to a curve at any point (x,y) on it is given by , where x>0 and y>0. If the curve passes through the point, find the equation of the curve.