If \[\frac{d}{dx}\left[ x^n - a_1 x^{n - 1} + a_2 x^{n - 2} + . . . + \left( - 1 \right)^n a_n \right] e^x = x^n e^x\] then the value of ar, 0 < r ≤ n, is equal to
[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined
If y = xn−1 log x then x2 y2 + (3 − 2n) xy1 is equal to
[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined
If xy − loge y = 1 satisfies the equation \[x\left( y y_2 + y_1^2 \right) - y_2 + \lambda y y_1 = 0\]
[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined
If y2 = ax2 + bx + c, then \[y^3 \frac{d^2 y}{d x^2}\] is
[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined
\[\frac{y}{x}\cos\left( \frac{y}{x} \right) dx - \left\{ \frac{x}{y}\sin\left( \frac{y}{x} \right) + \cos\left( \frac{y}{x} \right) \right\} dy = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[xy \log\left( \frac{x}{y} \right) dx + \left\{ y^2 - x^2 \log\left( \frac{x}{y} \right) \right\} dy = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\left( 1 + e^{x/y} \right) dx + e^{x/y} \left( 1 - \frac{x}{y} \right) dy = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\left( x^2 + y^2 \right)\frac{dy}{dx} = 8 x^2 - 3xy + 2 y^2\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
(x2 − 2xy) dy + (x2 − 3xy + 2y2) dx = 0
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[x\frac{dy}{dx} = y - x \cos^2 \left( \frac{y}{x} \right)\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[x\frac{dy}{dx} - y = 2\sqrt{y^2 - x^2}\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[x \cos\left( \frac{y}{x} \right) \cdot \left( y dx + x dy \right) = y \sin\left( \frac{y}{x} \right) \cdot \left( x dy - y dx \right)\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
(x2 + 3xy + y2) dx − x2 dy = 0
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[\left( x - y \right)\frac{dy}{dx} = x + 2y\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
(2x2 y + y3) dx + (xy2 − 3x3) dy = 0
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[x\frac{dy}{dx} - y + x \sin\left( \frac{y}{x} \right) = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
\[y dx + \left\{ x \log\left( \frac{y}{x} \right) \right\} dy - 2x dy = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Solve the following initial value problem:
(x2 + y2) dx = 2xy dy, y (1) = 0
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Solve the following initial value problem:
\[x e^{y/x} - y + x\frac{dy}{dx} = 0, y\left( e \right) = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Solve the following initial value problem:
\[\frac{dy}{dx} - \frac{y}{x} + cosec\frac{y}{x} = 0, y\left( 1 \right) = 0\]
[9] Differential Equations
Chapter: [9] Differential Equations
Concept: undefined >> undefined
