Question

1. Find the general solution to the differential equation y''+ xy' + x^2 y = 0 using power series techniques

Answer #1

3. Find the general solution to the differential equation:
(x^2 + 1/( x + y) + y cos(xy)) dx + (y ^2 + 1 / (x + y) + x
cos(xy)) dy = 0

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.

Find the power series solution of the differential equation
y"-xy'+6y=0 about the ordinary point x=0

Given that y=e^x is a solution of the equation (x-1)y''-xy'+y=0,
find the general solution to (x-1)y''-xy'+y=1.

Find the general solution near x = 0 of y'' - xy' + 2y = 0.
(Power series, recursive formula problem)

Find two solutions of a power series for the differential
equation y'' - xy = 0 surrounding the ordinary point x=0

Consider the differential equation x2y''+xy'-y=0,
x>0.
a. Verify that y(x)=x is a solution.
b. Find a second linearly independent solution using the method
of reduction of order. [Please use y2(x) =
v(x)y1(x)]

Find the general solution to the differential equation: y’’ – 6
y’ + 13y = 0
Find the general solution to the differential equation: y’’ +
5y’ + 4y = x + cos(x)

Given the second-order differential equation
y''(x) − xy'(x) + x^2 y(x) = 0
with initial conditions
y(0) = 0, y'(0) = 1.
(a) Write this equation as a system of 2 first order
differential equations.
(b) Approximate its solution by using the forward Euler
method.

Find the solution of the Differential Equation
X^2y''-xy'+y=x

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