Consider the equation: x2 y''-6y=0 A. Could you solve this ODE using Homogeneous Linear Equations with...

Consider the equation: x² y''-6y=0

A. Could you solve this ODE using Homogeneous Linear Equations with Constant Coefficients? Explain.

B. Note that y₁=x^₃ is a solution of the ODE. Using reduction of order, find a solution y₂ such that { y₁, y₂} is linearly independent.

C. Prove that{y₁, y₂} is linearly independent.

D.What is the general solution?

Expert Solution

milcah answered 2 years ago

solve this equation y''-6y'+8y=1 when y(0)=1, y'(0)=7

non-homogeneous ODE. solve this equation analytically. -2y''+5y'+3y=exp(-0.2x) b.c y'(0)=1, y'(10)=-y(10)

Solve the following differential equations. i) y'''-6y''+10y'=0 ii) dy/dx= x2/(1+y2) with y(1)=3 iii) (x2-2y)y'+2x+2xy=0 iv) Use...

Solve the following differential equations. i) y'''-6y''+10y'=0 ii) dy/dx= x2/(1+y2) with y(1)=3 iii) (x2-2y)y'+2x+2xy=0 iv) Use substitution to solve t2y'+2ty=y5 for t>0

Solve: y' = (y2-6y-16)x2 y(4) = 3

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

Consider the differential equation (x 2 + 1)y ′′ − 4xy′ + 6y = 0. (a)...

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...

Consider the following second-order ODE, y"+1/4y=0 with y(0) = 1 and y'(0)=0. Transform this unique equation...

Consider the following second-order ODE, y"+1/4y=0 with y(0) = 1 and y'(0)=0. Transform this unique equation into a system of two 1st-order ODEs. Solve the obtained system for t in [0,0.6] with h = 0.2 by MATLAB using Euler Method or Improved Euler Method.

second order linear non-homogeneous solve the following equations d2y/dx2+ y=5ex-4x2

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....

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 laplace transform to solve the initial value problem. y"-6y'+9y=t. Y(0)=0, y'(0)=1

Question