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Mathematics
\[\frac{dy}{dx} + y = \cos x\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\frac{dy}{dx} + 2y = \sin x\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
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\[\frac{dy}{dx}\] = y tan x − 2 sin x
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\left( 1 + x^2 \right)\frac{dy}{dx} + y = \tan^{- 1} x\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\frac{dy}{dx}\] + y tan x = cos x
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\frac{dy}{dx}\] + y cot x = x2 cot x + 2x
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\left( 1 + y^2 \right) + \left( x - e^{tan^{- 1} y} \right)\frac{dy}{dx} = 0\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{1}{\left( x^2 - 1 \right) \sqrt{x^2 + 1}} \text{ dx }\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
Integration of \[\frac{1}{1 + \left( \log_e x \right)^2}\] with respect to loge x is
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int \left| x \right|^3 dx\] is equal to
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{8x + 13}{\sqrt{4x + 7}} \text{ dx }\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{1 + x + x^2}{x^2 \left( 1 + x \right)} \text{ dx}\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
Find the shortest distance between the lines
\[\frac{x - 2}{- 1} = \frac{y - 5}{2} = \frac{z - 0}{3} \text{ and } \frac{x - 0}{2} = \frac{y + 1}{- 1} = \frac{z - 1}{2} .\]
Chapter: [11] Three - Dimensional Geometry
Concept: undefined >> undefined
Concept: undefined >> undefined
Find the shortest distance between the lines
\[\frac{x + 1}{7} = \frac{y + 1}{- 6} = \frac{z + 1}{1} \text{ and } \frac{x - 3}{1} = \frac{y - 5}{- 2} = \frac{z - 7}{1} .\]
Chapter: [11] Three - Dimensional Geometry
Concept: undefined >> undefined
Concept: undefined >> undefined
Find the shortest distance between the lines
\[\frac{x - 1}{2} = \frac{y - 3}{4} = \frac{z + 2}{1}\] and
\[3x - y - 2z + 4 = 0 = 2x + y + z + 1\]
Chapter: [11] Three - Dimensional Geometry
Concept: undefined >> undefined
Concept: undefined >> undefined
Differentiate sin(log sin x) ?
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined
Concept: undefined >> undefined
If `x=a (cos t +t sint )and y= a(sint-cos t )` Prove that `Sec^3 t/(at),0<t< pi/2`
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined
Concept: undefined >> undefined
If x = a (1 + cos θ), y = a(θ + sin θ), prove that \[\frac{d^2 y}{d x^2} = \frac{- 1}{a}at \theta = \frac{\pi}{2}\]
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined
Concept: undefined >> undefined
Differentiate `log [x+2+sqrt(x^2+4x+1)]`
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined
Concept: undefined >> undefined
