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Mathematics
Find `int (sin^2 x - cos^2x)/(sin x cos x) dx`
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
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Evaluate: `int_0^π (x sin x)/(1 + cos^2x) dx`.
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
Evaluate `int_0^(3/2) |x sin pix|dx`
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
Prove that x2 – y2 = c(x2 + y2)2 is the general solution of the differential equation (x3 – 3xy2)dx = (y3 – 3x2y)dy, where C is parameter
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
Find `int (2x)/((x^2 + 1)(x^4 + 4))`dx
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
Find `int((3 sin x - 2) cos x)/(13 - cos^2 x- 7 sin x) dx`
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\frac{y}{x}\cos\left( \frac{y}{x} \right) dx - \left\{ \frac{x}{y}\sin\left( \frac{y}{x} \right) + \cos\left( \frac{y}{x} \right) \right\} dy = 0\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[xy \log\left( \frac{x}{y} \right) dx + \left\{ y^2 - x^2 \log\left( \frac{x}{y} \right) \right\} dy = 0\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\left( 1 + e^{x/y} \right) dx + e^{x/y} \left( 1 - \frac{x}{y} \right) dy = 0\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\left( x^2 + y^2 \right)\frac{dy}{dx} = 8 x^2 - 3xy + 2 y^2\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
(x2 − 2xy) dy + (x2 − 3xy + 2y2) dx = 0
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[x\frac{dy}{dx} = y - x \cos^2 \left( \frac{y}{x} \right)\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[x\frac{dy}{dx} - y = 2\sqrt{y^2 - x^2}\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[x \cos\left( \frac{y}{x} \right) \cdot \left( y dx + x dy \right) = y \sin\left( \frac{y}{x} \right) \cdot \left( x dy - y dx \right)\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
(x2 + 3xy + y2) dx − x2 dy = 0
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\left( x - y \right)\frac{dy}{dx} = x + 2y\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
(2x2 y + y3) dx + (xy2 − 3x3) dy = 0
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[x\frac{dy}{dx} - y + x \sin\left( \frac{y}{x} \right) = 0\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[y dx + \left\{ x \log\left( \frac{y}{x} \right) \right\} dy - 2x dy = 0\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
