Given the differential equation y’’ +5y’+6y=te^t with start
value y(0) = 0 and y’(0). Let Y(s) be the Laplace transformed of
y(t).
a) Find an expression for Y(s)
b) Find the solution to the equation by using inverse Laplace
transform.
Consider the differential equation:
y'(x)+3xy+y^2=0.
y(1)=0. h=0.1
Solve the differential equation to determine y(1.3)
using:
a. Euler Method
b. Second order Taylor series method
c. Second order Runge Kutta method
d. Fourth order Runge-Kutta method
e. Heun’s predictor corrector method
f. Midpoint method
Determine the solution to the initial value differential
equation;
y′=0.0015y(1100−y), y(0)=32
1. y(x) = ?
2. What is the maximum value of this function. In other words,
evaluate: lim x-> inf y(x)
3. Determine x for which y(x) reaches 86% of its maximum
value.
Consider the differential equation
(x
2 + 1)y
′′ − 4xy′ + 6y = 0.
(a) Determine all singular points and find a minimum value for the
radius of convergence of
a power series solution about x0 = 0.
(b) Use a power series expansion y(x) = ∑∞
n=0
anx
n
about the ordinary point x0 = 0, to find
a general solution to the above differential equation, showing all
necessary steps including the
following:
(i) recurrence relation;
(ii) determination...
Power series
Find the particular solution of the differential equation:
(x^2+1)y"+xy'-4y=0 given the boundary conditions x=0, y=1 and y'=1.
Use only the 7th degree term of the solution. Solve for y at x=2.
Write your answer in whole number.
1.(4-x^2)y''+2y=0, x0=0
(a) Seek power series solutions of the given differential
equation about the given point x0; find the recurrence
relation.
(b) Find the first four terms in each of two solutions y1 and y2
(unless the series terminates sooner)
. (c) By evaluating the Wronskian W(y1, y2)(x0), show that y1
and y2 form a fundamental set of solutions.
(d) If possible, find the general term in each solution.