Question
In: Advanced Math
Order reduction Generate the general solution for each of the given equations if y_1 is known...
Order reduction
Generate the general solution for each of the given equations if y_1 is known to be a solution.
1. y``-4y'+4y=0, y1=e^2x
2. y''+2y'+y=0, y1=xe^-x
3.x^2y''-xy'+2y=0, y1=xsin(lnx)
Solutions
Colby Messinger answered 1 year agoRelated Solutions
Topic: Differential Equations; reduction order. The indicated fuction y1(x) is a solution of the given differential...
Topic: Differential Equations; reduction
order.
The indicated fuction y1(x) is a solution of the
given differential equation. Use the reduction order
technique to find a second solution y2(x).
xy'' + y' = 0; y1= ln(x)
Please, explain deeply each part of the solution, and include
complete algebraic explanation as well. Otherwise, the answer will
be negatively replied.
Find the general solution using REDUCTION OF ORDER. and the Ansatz of the form y=uy1 =...
Find the general solution using REDUCTION OF ORDER. and
the Ansatz of the form y=uy1 = y=ue-x
(2x+1)y'' -2y' - (2x+3)y = (2x+1)2 ; y1 =
e-x
Thank you in advance
Use the method of reduction of order to find a second solution y2 of the given...
Use the method of reduction of order to find a second solution
y2 of the given differential equation such that {y1, y2} is a
fundamental set of solutions on the given interval.
t2y′′ +2ty′ −2y=0, t > 0, y1(t)=t
(a) Verify that the two solutions that you have obtained are
linearly independent.
(b) Let y(1) = y0, y′(1) = v0. Solve the initial value problem.
What is the longest interval on which the initial value problem is
certain to have...
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order...
The indicated function y1(x) is a solution of the
given differential equation. Use reduction of order to find
y2(x)
x2y'' − xy' + 17y = 0 ;
y1=xsin(4In(x))
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order...
The indicated function y1(x) is a solution of the given
differential equation. Use reduction of order or formula (5) in
Section 4.2, y2 = y1(x) e−∫P(x) dx y 2 1 (x) dx (5) as instructed,
to find a second solution y2(x). x2y'' − xy' + 26y = 0; y1 = x
sin(5 ln(x)).......................................
Partial Differential Equations (a) Find the general solution to the given partial differential equation and (b)...
Partial Differential Equations
(a) Find the general solution to the given partial differential
equation and (b) use it to find the solution satisfying the given
initial data.
Exercise 1. 2∂u ∂x − ∂u ∂y = (x + y)u
u(x, x) = e −x 2
Exercise 2. ∂u ∂x = −(2x + y) ∂u ∂y
u(0, y) = 1 + y 2
Exercise 3. y ∂u ∂x + x ∂u ∂y = 0
u(x, 0) = x 4
Exercise 4. ∂u...
Problem 3: Find a second solution by reduction of order - nonhomogeneous The given function y1(x)...
Problem 3: Find a second solution by reduction of order -
nonhomogeneous
The given function y1(x) is a solution of the associated
homogeneous equation. Use the reduction of order method to find a
solution y(x) = u(x)y1(x) of the nonhomogeneous equation.
1. x^2y'' + xy'−4y = x^3, y1 = x^2
2. 2x^2*y'' + 3xy'−y = 1/x , y1 = x^(1/2)
Use ‘Reduction of Order’ to find a second solution y2 to the given ODEs: (a) y′′+2y′+y=0,...
Use ‘Reduction of Order’ to find a second solution y2 to the
given ODEs:
(a) y′′+2y′+y=0, y1 =xe−x
(b) y′′+9y=0, y1 =sin3x
(c) x2y′′+2xy′−6y=0, y1 =x2
(d) xy′′ +y′ =0, y1 =lnx
Determine the general solution of the differential equations. Write out the solution ? explicitly as a...
Determine the general solution of the differential equations.
Write out the solution ? explicitly as a function of ?.
(a) 3?^2?^2 ??/?? = 2?−1
(b) 2 ??/?? + 3? = ?^−2? − 5
For each of the following differential equations, find the particular solution that satisfies the additional given...
For each of the following differential equations, find the
particular solution that satisfies the additional given property
(called an initial condition).
y'y = x + 1
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