PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

Solution of the differential equation \[\frac{dy}{dx} + \frac{y}{x}=\sin x\] is

The solution of the differential equation \[2x\frac{dy}{dx} - y = 3\] represents

The solution of the differential equation \[x\frac{dy}{dx} = y + x \tan\frac{y}{x}\], is

If m and n are the order and degree of the differential equation \[\left( y_2 \right)^5 + \frac{4 \left( y_2 \right)^3}{y_3} + y_3 = x^2 - 1\], then

The solution of the differential equation \[\frac{dy}{dx} + 1 = e^{x + y}\], is

The solution of x² + y²  \[\frac{dy}{dx}\]= 4, is

The solution of the differential equation x dx + y dy = x² y dy − y² x dx, is

The solution of the differential equation (x² + 1) \[\frac{dy}{dx}\] + (y² + 1) = 0, is

The solution of the differential equation \[\frac{dy}{dx} - ky = 0, y\left( 0 \right) = 1\] approaches to zero when x → ∞, if

The solution of the differential equation \[\left( 1 + x^2 \right)\frac{dy}{dx} + 1 + y^2 = 0\], is

The solution of the differential equation \[\frac{dy}{dx} = \frac{x^2 + xy + y^2}{x^2}\], is

The number of arbitrary constants in the general solution of differential equation of fourth order is

The number of arbitrary constants in the particular solution of a differential equation of third order is

Which of the following differential equations has y = x as one of its particular solution?

The general solution of the differential equation \[\frac{dy}{dx} = e^{x + y}\], is

The general solution of the differential equation \[\frac{y dx - x dy}{y} = 0\], is

The general solution of a differential equation of the type \[\frac{dx}{dy} + P_1 x = Q_1\] is

The general solution of the differential equation e^x dy + (y e^x + 2x) dx = 0 is

Prove that the function f(x) = log_a x is increasing on (0, ∞) if a > 1 and decreasing on (0, ∞), if 0 < a < 1 ?