In: Advanced Math

y"+3xy'-4y=0

Solve the differential equation.

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 the following differential equation:
y''+4y'+4y=u(t-1)-u(t-3), y(0)=0, y'(0)=0

Solve the differential equation.
y''-3y'-4y=5e^4x
initial conditions:
y(0)=2
y'(0)=4

Solve the differential equation.
y'''-4y''+5y'-2y=0
Initial Conditions:
y(0)=4
y'(0)=7
y''(0)=11

Solve the ordinary differential equation analytically:
y''-4y-+3y = 5cos(x) + e^(2x)
y(0)=1, y'(0)=0

Differential Equations
Use a series solution to solve the IVP .
y′′−4y= 0
y(0) = 3
y′(0) = 5.
(Your answer will use one or more series.)

Solve 3xy'' + y' - y = 0 by the Method of Frobenius.

Use Laplace Transforms to solve the following second-order
differential equation:
y"-3y'+4y=xe2x where y'(0)=1 and y(0)=2

Solve the differential equation. y'' − 8y' + 20y = te^t, y(0) =
0, y'(0) = 0
(Answer using fractions)

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

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