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Evaluate: dy/dx = (1 + x^2)(1 + y^2)
Correct Answer Is : Tan ^-1 y = x + (x^3/3)+ c Evaluate : ylog y dx - xdy = 0 Correct Answer Is : Y = e^cx Evaluate: cos(dy/dx) = a(a Є R); y = 1 when x = 0. Correct Answer Is : Cos(y - 1/x) = a Find the equation of a curve passing through the point (0 , 0) and whose differential equation is y` = e^ sin x. Correct Answer Is : 2y - 1 = e^x (sin x - cos x) The slope of a tangent to the curve in the coordinate axis is given by the relation: Correct Answer Is : Dy/dx Evaluate: y` = (x + y/x) Correct Answer Is : Y = xlog x + Cx True or false: the differential equation of the family of hyperbolas having foci on x-axis and centre at the origin xyy" + x(y`)^2 - yy` = 0. Correct Answer Is : TRUE Evaluate: (x^2 - y^2)dx + 2xy dy = 0 Correct Answer Is : (x^2 + y^2) = cx