Question

Find the general solution of the second-order nonhomogeneous equation:

ty″ − y′ = (t^2) + t

Answer #1

- please like

Find a general solution to the given equation for t<0
y"(t)-1/ty'(t)+5/t^2y(t)=0

A nonhomogeneous equation and a particular solution are given.
Find a general solution for the equation.
y''+5y'+6y=24x^(2)+40x+8+12e^(x), y_p(x)=e^(x)+4x^(2)
The general solution is y(x)=
(Do not use d, D, e, E, i, or I as arbitrary constants since
these letters already have defined meanings.)

Find the general solution to the given differential
equation. 1+(1+ty)e^ty+(1+t^2e^ty) dy/dt=0

y′′(t) +ty′(t)−2y(t) = 2, y(0) = 0,y′(0) = 0 . This is a
non-homogeneous linear second-order differential equation
withnon-constantcoefficients andnotof Euler type.
(a) Write the Laplace transform of the Initial Value Problem
above.
(b) Find a closed formula for the Laplace transformL(y(t)).
(c) Find the unique solutiony(t) to the Initial Value
Problem

The nonhomogeneous equation t2 y′′−2 y=29 t2−1, t>0, has
homogeneous solutions y1(t)=t2, y2(t)=t−1. Find the particular
solution to the nonhomogeneous equation that does not involve any
terms from the homogeneous solution.

The nonhomogeneous equation t2 y′′−2 y=19
t2−1, t>0, has homogeneous solutions
y1(t)=t2, y2(t)=t−1. Find the particular
solution to the nonhomogeneous equation that does not involve any
terms from the homogeneous solution.
Enter an exact answer.
Enclose arguments of functions in parentheses. For example,
sin(2x).
y(t)=

Use variation of parameters to find a general solution to the
differential equation given that the functions y 1 and y 2 are
linearly independent solutions to the corresponding homogeneous
equation for t>0.
ty"-(t+1)y'+y=30t^2 ; y1=e^t , y2=t+1
The general solution is y(t)= ?

Find the general solution of the equation:
y" + 4y = t^2 + 3e^t
salisfying y(0) = 1 and y'(0) = 0

Consider the following second-order differential equation:
?"(?)−?′(?)−6?(?)=?(?)
(1) Let ?(?)=−12e^t. Find the general solution to the above
equation.
(2) Let ?(?)=−12.
a) Convert the above second-order differential equation into a
system of first-order differential equations.
b) For your system of first-order differential equations in part
a), find the characteristic equation, eigenvalues and their
associated eigenvectors.
c) Find the equilibrium for your system of first-order
differential equations. Draw a phase diagram to illustrate the
stability property of the equilibrium.

Solve the following second order differential equations:
(a) Find the general solution of y'' − 2y' = sin(3x) using the
method of undetermined coefficients.
(b) Find the general solution of y'' − 2y'− 3y = te^−t using the
method of variation of parameters.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 32 minutes ago

asked 38 minutes ago

asked 38 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago