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Solve the following differential equation:
\[y e^\frac{x}{y} dx = \left( x e^\frac{x}{y} + y^2 \right)dy, y \neq 0\]
Chapter: [9] Differential Equations
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Solve the following differential equation:
\[\left( 1 + y^2 \right) \tan^{- 1} xdx + 2y\left( 1 + x^2 \right)dy = 0\]
Chapter: [9] Differential Equations
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\[\frac{dy}{dx} = y \tan 2x, y\left( 0 \right) = 2\]
Chapter: [9] Differential Equations
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\[2x\frac{dy}{dx} = 3y, y\left( 1 \right) = 2\]
Chapter: [9] Differential Equations
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\[xy\frac{dy}{dx} = y + 2, y\left( 2 \right) = 0\]
Chapter: [9] Differential Equations
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\[\frac{dy}{dx} = 2 e^x y^3 , y\left( 0 \right) = \frac{1}{2}\]
Chapter: [9] Differential Equations
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\[\frac{dr}{dt} = - rt, r\left( 0 \right) = r_0\]
Chapter: [9] Differential Equations
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\[\frac{dy}{dx} = y \sin 2x, y\left( 0 \right) = 1\]
Chapter: [9] Differential Equations
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\[\frac{dy}{dx} = y \tan x, y\left( 0 \right) = 1\]
Chapter: [9] Differential Equations
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\[2x\frac{dy}{dx} = 5y, y\left( 1 \right) = 1\]
Chapter: [9] Differential Equations
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\[\frac{dy}{dx} = 2 e^{2x} y^2 , y\left( 0 \right) = - 1\]
Chapter: [9] Differential Equations
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\[\cos y\frac{dy}{dx} = e^x , y\left( 0 \right) = \frac{\pi}{2}\]
Chapter: [9] Differential Equations
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\[\frac{dy}{dx} = 2xy, y\left( 0 \right) = 1\]
Chapter: [9] Differential Equations
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\[\frac{dy}{dx} = 1 + x^2 + y^2 + x^2 y^2 , y\left( 0 \right) = 1\]
Chapter: [9] Differential Equations
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\[xy\frac{dy}{dx} = \left( x + 2 \right)\left( y + 2 \right), y\left( 1 \right) = - 1\]
Chapter: [9] Differential Equations
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\[\frac{dy}{dx} = 1 + x + y^2 + x y^2\] when y = 0, x = 0
Chapter: [9] Differential Equations
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\[2\left( y + 3 \right) - xy\frac{dy}{dx} = 0\], y(1) = −2
Chapter: [9] Differential Equations
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Solve the differential equation \[x\frac{dy}{dx} + \cot y = 0\] given that \[y = \frac{\pi}{4}\], when \[x=\sqrt{2}\]
Chapter: [9] Differential Equations
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Solve the differential equation \[\left( 1 + x^2 \right)\frac{dy}{dx} + \left( 1 + y^2 \right) = 0\], given that y = 1, when x = 0.
Chapter: [9] Differential Equations
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Solve the differential equation \[\frac{dy}{dx} = \frac{2x\left( \log x + 1 \right)}{\sin y + y \cos y}\], given that y = 0, when x = 1.
Chapter: [9] Differential Equations
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