MATH2021: Vector Calculus and Differential Equations Semester 1, 2023 Assignment 2

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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 )  + y3  = 0

y  = (x - y ) cos y4

(x + y) = (x3 - y2 ) sin(xy)

 

dy x

 

x2 + 1

2y

 

First Order Linear Equations

2.  Solve the following Linear First Order Linear Equation using the Integrating Factor

(1 + x3 )  = 2 - 3x2y

3.  Use the method of Variation of Parameters to find the general solution of the following

 

- y = xe-北 dx

Laplace Transforms

4.  Use Laplace transforms to solve the initial value problem

y\\ - 4y = e3t

 

y(0) = 0

y\ (0) = 0

 

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)

 


2023-06-03