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Mathematics
(x2 − y2) dx − 2xy dy = 0
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\frac{dy}{dx} = \frac{x + y}{x - y}\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
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\[2xy\frac{dy}{dx} = x^2 + y^2\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[x^2 \frac{dy}{dx} = x^2 - 2 y^2 + xy\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[xy\frac{dy}{dx} = x^2 - y^2\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
y ex/y dx = (xex/y + y) dy
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[x^2 \frac{dy}{dx} = x^2 + xy + y^2 \]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
(y2 − 2xy) dx = (x2 − 2xy) dy
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
2xy dx + (x2 + 2y2) dy = 0
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
3x2 dy = (3xy + y2) dx
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\frac{dy}{dx} = \frac{x}{2y + x}\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
(x + 2y) dx − (2x − y) dy = 0
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\frac{dy}{dx} = \frac{y}{x} - \sqrt{\frac{y^2}{x^2} - 1}\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
Solve the following differential equations:
\[\frac{dy}{dx} = \frac{y}{x}\left\{ \log y - \log x + 1 \right\}\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\frac{dy}{dx} = \frac{y}{x} + \sin\left( \frac{y}{x} \right)\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\left[ x\sqrt{x^2 + y^2} - y^2 \right] dx + xy\ dy = 0\]
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
Find the particular solution of the differential equation \[\frac{dy}{dx} = \frac{xy}{x^2 + y^2}\] given that y = 1 when x = 0.
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
Solve the following initial value problem:-
\[y' + y = e^x , y\left( 0 \right) = \frac{1}{2}\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
Solve the following initial value problem:-
\[x\frac{dy}{dx} - y = \log x, y\left( 1 \right) = 0\]
Chapter: [9] Differential Equations
Concept: undefined >> undefined
Concept: undefined >> undefined
