DIFFERENTIAL EQUATIONS (Practice Problems)
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1
Find the particular solution of dy/dx = [sin (x^(1/2))]/y^(1/2) that passes through a point.
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2
Solve the first-order differential equation: y[ln (y/x) - 1] dx + x dy = 0.
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3
Solve the first-order differential equation: 3 (t^2 + t^4) dx/dt = tx (t^3 x^3 - 2t^2 - 2).
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4
Find the particular solution of the first-order differential equation: dy/dx = -y csc x - sin x.
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5
Particular solution of the differential equation: (sec^2 y + sin x - 3xy^2) dy/dx = y (y^2 - cos x).
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6
Solve the first-order differential equation.
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7
Find the general solution of the first-order differential equation.
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8
Find the particular solution of y''' - 2y'' - 7y' - 4y = 0, y = 0, y' = 1, and y'' = -1 at x = 0.
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9
Find the general solution of y''' - 2y'' - 7y' - 4y = 20e^(-x) + 4.
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10
Find the general solution of 3y'' + 2y' + 4y = e^(-x/3) sec^2 (sqrt(11)x/3).
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11
Power Series Solution to Differential Equations Near an Ordinary Point (Example)
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12
Power Series Solution to Differential Equations Near a Singular Point (Example)
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13
Solution by Laplace Transform of Differential Equations with a Discontinuous Forcing Function
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14
Solution by Laplace Transform of Differential Equations with an Impulse Forcing Function (Example)
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15
Solution by Laplace Transform and Convolution Theorem of Differential Equations (Example)
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16
Solution by Laplace Transform of Integral or Integrodifferential Equations (Example)
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