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MATH2021: Vector Calculus and Differential Equations Semester 1, 2023 Assignment 2
发布时间:2023-06-03
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Assignment 2
MATH2021: Vector Calculus and Differential Equations
Semester 1, 2023
Differential Equations
Separable Equations
1. Which of the following differential equations are Separable? Solve the ones that are separable:
(1 + x2 ) |
y |
(x + y) |
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2y |
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First Order Linear Equations
2. Solve the following Linear First Order Linear Equation using the Integrating Factor
(1 + x3 ) |
3. Use the method of Variation of Parameters to find the general solution of the following
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Laplace Transforms
4. Use Laplace transforms to solve the initial value problem
y\\ - 4y = e3t |
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y(0) = 0 |
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Power Series Solutions
5. Find the power series solution of the differential equation
o y(x) = an xn n=0 |
. Determine the recurrence relation satisfied by the coefficients.
Use it to calculate the first four non-zero terms of the series.
y(x) = a0 cos(3x) + a1 sin(3x) |