In: Advanced Math

Consider the differential equation x′=[2 4

-2 −2],

with x(0)=[1 1]

Solve the differential equation where x=[x(t)y(t)].

x(t)=

y(t)=

please be as clear as possible especially when solving for c1 and c2 that's the part i need help the most

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

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...

5. Consider the differential equation
xy^5/2 +1+x^2y^3/2dy/dx =0
(a) Show that this differential equation is not exact.
(b) Find a value for the constant a such that, when you multiply
the d.e. through by xa, it becomes exact. Show your working. Do NOT
solve the resulting differential equation.
6. Consider the differential equation
(D − 3)(D − 4)y = 0.
(a) Solve this d.e., showing brief working.
(b) How many solutions does this d.e. have? Justify your
answer.
(c) How...

Solve this differential equation
y''+(-4-2-2)y'+(4+4+4+4)y=x
y(0)=3-2
y'(0)=2-3
Answer it as y(x)=... and motivate all the steps of the
calculation

For
the differential equation (2 -x^4)y" + (2*x -4)y' + (2*x^2)y=0.
Compute the recursion formula for the coefficients of the power
series solution centered at x(0)=0 and use it to compute the first
three nonzero terms of the solution with y(0)= 12 , y'(0) =0

Solve this differential equation using
Matlab
yy' + xy2 =x , with y(0)=5 for x=0 to 2.5 with a step
size 0.25
(a) Analytical
(b) Euler
(c) Heun
d) 4th order R-K method
Display all results on the same graph

Solve the following differential equation using the power series
method.
(1+x^2)y''-y'+y=0

Solve the differential equation
y''+y'-2y=3, y(0)=2, y'(0) = -1

Solve the differential equation
1. a) 2xy"+ y' + y = 0
b) (x-1)y'' + 3y = 0

Solve the following first order differential equations:
(a) 2/?^ ???/?? = 4?^2? ; ?(0) = −1/ 3
(b) ??/?? + ? = ? ; ?(0) = 5
(c) ??/?? + ? /? = ? 3 ; ? ( 1/2 ) = 1

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