Consider a Cauchy-Euler equation x^2y''- xy' +y =x^3 for
x>0.
a) Rewrite the equation as constant- coefficeint equation by
substituting x = e^t.
b) Solve it when x(1)=0, x'(1)=1.
exampleInput.txt
1 2 3
0 2 3 4
0 1 3 5
0 1 2 6
1 5 6 8
2 4 6 7
3 4 5 9 10
5 8 9
4 7 9
6 7 8
6
How can I detect when 'cin' starts reading from a new line. The
amount of numbers in each row is unknown. I need them in type 'int'
to use the data.
1) . Solve the IVP:
y^''+6y^'+5y=0, y(0)=1, y^' (0)=3
2. Find the general solution to each of the following:
a) y^''+2y^'+5y=e^2x
b) y^''+2x/(x^2+1) y'=x
c) y^''+4y=1/(sin(2x)) (use variation of parameters)
[2 marks] Suppose that the characteristic polynomial of the
following Cauchy-Euler equation
x2 y′′ +
αx y′ + β y
= 0
has roots m1 = 2 − 3i, and
m2 = 2 + 3i. Find α and
β.
Enter the values of α and β (in that order) into
the answer box below, separated with a comma.
for the matrix, A= [1 2 -1; 2 3 1; -1 -1 -2; 3 5 0]
a. calculate the transpose of A multiplied by A
b. find the eigenvectors and eigenvalues of the answer to a
c. Find the SVD of matrix A