Arts (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

Solve the differential equation \[\left( x + 2 y^2 \right)\frac{dy}{dx} = y\], given that when x = 2, y = 1.

Find the general solution of the differential equation \[x\frac{dy}{dx} + 2y = x^2\]

Find the general solution of the differential equation \[\frac{dy}{dx} - y = \cos x\]

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

Find the particular solution of the differential equation \[\frac{dx}{dy} + x \cot y = 2y + y^2 \cot y, y ≠ 0\] given that x = 0 when \[y = \frac{\pi}{2}\].

Solve the following differential equation:- \[\left( \cot^{- 1} y + x \right) dy = \left( 1 + y^2 \right) dx\]

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Write a value of\[\int \cos^4 x \text{ sin x dx }\]

Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]

Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]

Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].

Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]