1) parabola 2) hyperbola 3) circle 4) ellipse Solution: (2) hyperbola \(\begin{array}{l}\frac{d y}{d x}=\frac{\left(1+y^{2}\right) x}{y\left(1+x^{2}\right)} \\ \Rightarrow \int \frac{2 y}{1+y}... View Article

The equation of curve through point (1, 0) which satisfies the differential equation (1 + y²) dx – xy dy = 0, is

1) x2 + y2 = 4 2) x2 – y2 = 1 3) 2x2 + y2 = 2 4) None... View Article

The solution of the differential equation (dy / dx) = (4x + y + 1)² is

1) (4x + y + 1) = tan (2x + C) 2) (4x + y + 1)2 = 2 tan... View Article

The solution of the differential equation (dy / dx) = [x – 2y + 1] / [2x – 4y] is

1) (x – 2y)2 + 2x = C 2) (x – 2y)2 + x = C 3) (x – 2y)... View Article

The solution of the differential equation 9y (dy/dx) + 4x = 0 is

1) (y2 / 9) + (x2 / 4) = c 2) (y2 / 4) + (x2 / 9) = c... View Article

The solution of the differential equation (x + y)² (dy / dx) = a² is

1) (x + y)2 (dy / dx) = (a2x / 2) + c 2) (x + y)2 (dy / dx)... View Article

The differential equation y (dy/dx) + x = c represents

1) a family of hyperbolas 2) a family of circles whose centres are on the y-axis 3) a family of... View Article

The solution of the differential equation dy / dx = [x – y + 3] / [2 (x – y) + 5] is

1) 2(x – y) + log (x – y) = x + C 2) 2(x – y) – log (x... View Article

The solution of the equation y – x (dy / dx) = a [y² + (dy / dx)] is

1) y = C (x + a)(1 – ay) 2) y = C (x + a)(1 + ay) 3) y... View Article

The solution of the differential equation dy / dx = [xy + y] / [xy + x] is

1) x + y = log (cy / x) 2) x + y = log (cxy) 3) x – y... View Article

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