Arts (English Medium) इयत्ता १२ - CBSE Question Bank Solutions for Mathematics

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.

y = e^2x (a + bx)

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.

y = e^x (a cos x + b sin x)

Find the particular solution of the differential equation (1 + e^2x) dy + (1 + y²) e^x dx = 0, given that y = 1 when x = 0.

Solve the differential equation  `ye^(x/y) dx = (xe^(x/y) + y^2)dy, (y != 0)`

Find a particular solution of the differential equation (x - y) (dx + dy) = dx - dy, given that y = -1, when x = 0. (Hint: put x - y = t)

The general solution of the differential equation `(y dx - x dy)/y = 0` is ______.

The general solution of a differential equation of the type  `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 ______.

Integrate the function `(3x^2)/(x^6 + 1)`

Integrate the function `1/sqrt(1+4x^2)`

Integrate the function `1/sqrt((2-x)^2 + 1)`

Integrate the function `1/sqrt(9 - 25x^2)`

Integrate the function `(3x)/(1+ 2x^4)`

Integrate the function `x^2/(1 - x^6)`

Integrate the function `(x - 1)/sqrt(x^2 - 1)`

Integrate the function `x^2/sqrt(x^6 + a^6)`

Integrate the function `(sec^2 x)/sqrt(tan^2 x + 4)`

Integrate the function `1/sqrt(x^2 +2x + 2)`

Integrate the function `1/(9x^2 + 6x + 5)`

Integrate the function `1/sqrt(7 - 6x - x^2)`