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

Solve the following differential equation:-

\[\frac{dy}{dx} + \left( \sec x \right) y = \tan x\]

Solve the following differential equation:-

\[x\frac{dy}{dx} + 2y = x^2 \log x\]

Solve the following differential equation:-

\[x \log x\frac{dy}{dx} + y = \frac{2}{x}\log x\]

Solve the following differential equation:-

(1 + x²) dy + 2xy dx = cot x dx

Solve the following differential equation:-

\[\left( x + y \right)\frac{dy}{dx} = 1\]

Solve the following differential equation:-

y dx + (x − y²) dy = 0

Solve the following differential equation:-

\[\left( x + 3 y^2 \right)\frac{dy}{dx} = y\]

Find a particular solution of the following differential equation:- \[\left( 1 + x^2 \right)\frac{dy}{dx} + 2xy = \frac{1}{1 + x^2}; y = 0,\text{ when }x = 1\]

Find a particular solution of the following differential equation:- (x + y) dy + (x − y) dx = 0; y = 1 when x = 1

Find a particular solution of the following differential equation:- x² dy + (xy + y²) dx = 0; y = 1 when x = 1

Find the equation of the curve passing through the point (1, 1) whose differential equation is x dy = (2x² + 1) dx, x ≠ 0.

Find the equation of a curve passing through the point (−2, 3), given that the slope of the tangent to the curve at any point (x, y) is `(2x)/y^2.`

Find the equation of a curve passing through the point (0, 0) and whose differential equation is \[\frac{dy}{dx} = e^x \sin x.\]

Find the equation of a curve passing through the point (0, 1). If the slope of the tangent to the curve at any point (x, y) is equal to the sum of the x-coordinate and the product of the x-coordinate and y-coordinate of that point.

Solve for x : tan^-1 (x - 1) + tan^-1x + tan^-1 (x + 1) = tan^-1 3x

Find : `int((2x-5)e^(2x))/(2x-3)^3dx`

Find: `int(x+3)sqrt(3-4x-x^2dx)`

Find `intsqrtx/sqrt(a^3-x^3)dx`

If a line makes angles 90°, 60° and θ with x, y and z-axis respectively, where θ is acute, then find θ.

Integrate the functions:

`(1+ log x)^2/x`