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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
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined
Concept: undefined >> undefined
If y = xn−1 log x then x2 y2 + (3 − 2n) xy1 is equal to
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined
Concept: undefined >> undefined
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If xy − loge y = 1 satisfies the equation \[x\left( y y_2 + y_1^2 \right) - y_2 + \lambda y y_1 = 0\]
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined
Concept: undefined >> undefined
If y2 = ax2 + bx + c, then \[y^3 \frac{d^2 y}{d x^2}\] is
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int e^{ax} \text{ sin} \left( bx + C \right) dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\text{ cos }\left( \text{ log x } \right) \text{ dx }\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int e^{2x} \cos \left( 3x + 4 \right) \text{ dx }\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{1}{x^3}\text{ sin } \left( \text{ log x }\right) dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int x^2 e^{x^3} \cos x^3 dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\frac{dy}{dx} + 2y = e^{3x}\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[4\frac{dy}{dx} + 8y = 5 e^{- 3x}\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\frac{dy}{dx} + 2y = 6 e^x\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\frac{dy}{dx} + y = e^{- 2x}\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[x\frac{dy}{dx} = x + y\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\frac{dy}{dx} + 2y = 4x\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
