In: Advanced Math

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

solve using forbenious series
3xy''+(2-x)y'-y=0

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 following equation: (3 − x^2 )y'' − 3xy' − y = 0
Derive the general solution of the given differential equation
about x = 0. Your answer should include a general formula for the
coefficents.

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

Solve the differential equation 2x^2y"-x(x-1)y'-y = 0 using the
Frobenius Method

Diff. equations
Consider the equation (x^2 − 2)y''+ 3xy'+ y = 0.
a) Find the general solution as a power series centered at x =
0. Write the first six nonzero terms of the solution. And write the
solution using sigma notation with a formula for the coefficients.
Write the two linearly independent solutions that form the general
solution.
b) Find a power series solution satisfying the initial
conditions y(0) = 2 and y' (0) = 3. Write the first...

Find two power series solutions of the given differential
equation about the point x=0
(x^2+2) y″+3xy'-y=0

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...

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 differential equation by using undetermined coefficient
method
y^''+9y=x^2e^x+6 , y(0)=1 and y^'(0)=1

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