\[x\frac{dy}{dx} + y = x e^x\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\frac{dy}{dx} + \frac{4x}{x^2 + 1}y + \frac{1}{\left( x^2 + 1 \right)^2} = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[x\frac{dy}{dx} + y = x \log x\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[x\frac{dy}{dx} - y = \left( x - 1 \right) e^x\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\frac{dy}{dx} + \frac{y}{x} = x^3\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\frac{dy}{dx} + y = \sin x\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\frac{dy}{dx} + y = \cos x\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\frac{dy}{dx} + 2y = \sin x\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\frac{dy}{dx}\] = y tan x − 2 sin x
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\left( 1 + x^2 \right)\frac{dy}{dx} + y = \tan^{- 1} x\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\frac{dy}{dx}\] + y tan x = cos x
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\frac{dy}{dx}\] + y cot x = x2 cot x + 2x
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\left( 1 + y^2 \right) + \left( x - e^{tan^{- 1} y} \right)\frac{dy}{dx} = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
If \[A = \begin{bmatrix}1 & - 2 & 0 \\ 2 & 1 & 3 \\ 0 & - 2 & 1\end{bmatrix}\] ,find A–1 and hence solve the system of equations x – 2y = 10, 2x + y + 3z = 8 and –2y + z = 7.
[4] Determinants
Chapter: [4] Determinants
Concept: undefined >> undefined
Find the shortest distance between the lines
\[\frac{x - 2}{- 1} = \frac{y - 5}{2} = \frac{z - 0}{3} \text{ and } \frac{x - 0}{2} = \frac{y + 1}{- 1} = \frac{z - 1}{2} .\]
[11] Three - Dimensional Geometry
Chapter: [11] Three - Dimensional Geometry
Concept: undefined >> undefined
Find the shortest distance between the lines
\[\frac{x + 1}{7} = \frac{y + 1}{- 6} = \frac{z + 1}{1} \text{ and } \frac{x - 3}{1} = \frac{y - 5}{- 2} = \frac{z - 7}{1} .\]
[11] Three - Dimensional Geometry
Chapter: [11] Three - Dimensional Geometry
Concept: undefined >> undefined
Find the shortest distance between the lines
\[\frac{x - 1}{2} = \frac{y - 3}{4} = \frac{z + 2}{1}\] and
\[3x - y - 2z + 4 = 0 = 2x + y + z + 1\]
[11] Three - Dimensional Geometry
Chapter: [11] Three - Dimensional Geometry
Concept: undefined >> undefined
Let f : W → W be defined as f(x) = x − 1 if x is odd and f(x) = x + 1 if x is even. Show that f is invertible. Find the inverse of f, where W is the set of all whole numbers.
[1] Relations and Functions
Chapter: [1] Relations and Functions
Concept: undefined >> undefined
Show that \[\begin{vmatrix}y + z & x & y \\ z + x & z & x \\ x + y & y & z\end{vmatrix} = \left( x + y + z \right) \left( x - z \right)^2\]
[4] Determinants
Chapter: [4] Determinants
Concept: undefined >> undefined
x + y = 1
x + z = − 6
x − y − 2z = 3
[4] Determinants
Chapter: [4] Determinants
Concept: undefined >> undefined
