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

Find the solution of the differential equation
\[x\sqrt{1 + y^2}dx + y\sqrt{1 + x^2}dy = 0\]

The integrating factor of the differential equation (x log x)
\[\frac{dy}{dx} + y = 2 \log x\], is given by

Integrating factor of the differential equation cos \[x\frac{dy}{dx} + y\] sin x = 1, is

The differential equation obtained on eliminating A and B from y = A cos ωt + B sin ωt, is

The equation of the curve whose slope is given by \[\frac{dy}{dx} = \frac{2y}{x}; x > 0, y > 0\] and which passes through the point (1, 1) is

The solution of the differential equation \[\frac{dy}{dx} = \frac{ax + g}{by + f}\] represents a circle when

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

The solution of the differential equation y₁ y₃ = y₂² is

The differential equation of the ellipse \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = C\] is

The differential equation satisfied by ax² + by² = 1 is

Which of the following transformations reduce the differential equation \[\frac{dz}{dx} + \frac{z}{x}\log z = \frac{z}{x^2} \left( \log z \right)^2\] into the form \[\frac{du}{dx} + P\left( x \right) u = Q\left( x \right)\]

The differential equation \[x\frac{dy}{dx} - y = x^2\], has the general solution

The differential equation
\[\frac{dy}{dx} + Py = Q y^n , n > 2\] can be reduced to linear form by substituting

Which of the following is the integrating factor of (x log x) \[\frac{dy}{dx} + y\] = 2 log x?

What is integrating factor of \[\frac{dy}{dx}\] + y sec x = tan x?

Integrating factor of the differential equation cos \[x\frac{dy}{dx} + y \sin x = 1\], is

Which of the following differential equations has y = C₁ e^x + C₂ e^−x as the general solution?

The integrating factor of the differential equation \[x\frac{dy}{dx} - y = 2 x^2\]

The integrating factor of the differential equation \[\left( 1 - y^2 \right)\frac{dx}{dy} + yx = ay\left( - 1 < y < 1 \right)\] is ______.

Classify the following measures as scalars and vectors:
(i) 15 kg
(ii) 20 kg weight
(iii) 45°
(iv) 10 meters south-east
(v) 50 m/sec²