In: Advanced Math

solve using forbenious series

3xy''+(2-x)y'-y=0

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

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

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

solve using series solutions
(x^+1)y''+xy'-y=0

using series to solve
differential equations
using series to solve
differential equations
1.) y’’-(e^5x)y’+xy=0,y(0)=2,y’(0)=1

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

Solve (1+e^x)dy/dx+(e^x)y=3x^2+1
Solve (x^3+y^3)dx+3xy^2 dy = 0
Solve (y-cos y)dx + (xsiny+x)dy = 0
Solve (1+ln x +y/x)dx = (1-lnx)dy
Solve (y^2+yx)dx - x^2dy =0
Solve (x^2+2y^2)dx = xydy
Solve Bernoulli's Equation x dy/dx + 2y = (x^4)(e^x)(y^2)
Solve Bernoulli's Equation (1+x^2) dy/dx = 2xy +(e^x)(y^2)
Solve IVP (3e^(x^2))dy + (xy^2)dx=0 ; y(1) = 2
Solve IVP dy/dx -2xy = e^(x^2) ; y(0)=0
Solve IVP (x^2+y^2)dx+(2xy)dy=0; y(1)=1
6. Mixture Problem
Initially 40 lb of salt is dissolved in a large...

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.

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...

x*y' '+y'-x*y=0
1> use Frobenious series solution to solve the ODE.

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