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In a bank principal increases at the rate of 5% per year. An amount of Rs 1000 is deposited with this bank, how much will it worth after 10 years (e0.5 = 1.648).
Chapter: [9] Differential Equations
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In a culture the bacteria count is 100000. The number is increased by 10% in 2 hours. In how many hours will the count reach 200000, if the rate of growth of bacteria is proportional to the number present.
Chapter: [9] Differential Equations
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If y(x) is a solution of the different equation \[\left( \frac{2 + \sin x}{1 + y} \right)\frac{dy}{dx} = - \cos x\] and y(0) = 1, then find the value of y(π/2).
Chapter: [9] Differential Equations
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Find the particular solution of the differential equation
(1 – y2) (1 + log x) dx + 2xy dy = 0, given that y = 0 when x = 1.
Chapter: [9] Differential Equations
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\[\frac{dy}{dx} = \left( x + y + 1 \right)^2\]
Chapter: [9] Differential Equations
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\[\frac{dy}{dx}\cos\left( x - y \right) = 1\]
Chapter: [9] Differential Equations
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\[\frac{dy}{dx} = \frac{\left( x - y \right) + 3}{2\left( x - y \right) + 5}\]
Chapter: [9] Differential Equations
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\[\frac{dy}{dx} = \left( x + y \right)^2\]
Chapter: [9] Differential Equations
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\[\left( x + y \right)^2 \frac{dy}{dx} = 1\]
Chapter: [9] Differential Equations
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\[\cos^2 \left( x - 2y \right) = 1 - 2\frac{dy}{dx}\]
Chapter: [9] Differential Equations
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\[\frac{dy}{dx} = \sec\left( x + y \right)\]
Chapter: [9] Differential Equations
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\[\frac{dy}{dx} = \tan\left( x + y \right)\]
Chapter: [9] Differential Equations
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(x + y) (dx − dy) = dx + dy
Chapter: [9] Differential Equations
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\[\left( x + y + 1 \right)\frac{dy}{dx} = 1\]
Chapter: [9] Differential Equations
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\[\frac{dy}{dx} + 1 = e^{x + y}\]
Chapter: [9] Differential Equations
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x2 dy + y (x + y) dx = 0
Chapter: [9] Differential Equations
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\[\frac{dy}{dx} = \frac{y - x}{y + x}\]
Chapter: [9] Differential Equations
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\[\frac{dy}{dx} = \frac{y^2 - x^2}{2xy}\]
Chapter: [9] Differential Equations
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\[x\frac{dy}{dx} = x + y\]
Chapter: [9] Differential Equations
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(x2 − y2) dx − 2xy dy = 0
Chapter: [9] Differential Equations
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