Question

x''+8x'+25x=10u(t).....x(0)=0....x'(0)=0 please solve this differential equation and show all steps including the characteristic equation.

Answer #1

Consider the differential equation x′=[2 −2 4 −2], with x(0)=[1
1] Solve the differential equation wherex=[x(t)y(t)]
please write as neat as possible better if typed and explain
clearly with step by step work

Please show all steps to the first order equation, using
infinity series.
a) solve:
y' - y = 0
b) solve:
(x-3)y' + 2y = 0

Please show all steps, thank you!
a) Verify that the functions below solve the system:
x(t) = c1e^5t + c2e^-t
y(t) = 2c1e^5t - c2e^-t
Do not solve the system
dx/dt = x + 2y
dy/dt = 4x +3y
b) Solve the system using Operator D elimination. Write the
answer both in scalar and vector form. Please show all steps!
dx/dt = x + 2y
dy/dt = 4x + 3y

Solve the 2nd Order Differential Equation using METHOD OF
REDUCTION
Please don't skip steps!
(x-1)y"-xy'+y=0 x>1 y1(x)=x

PLEASE solve with all the steps and correctly.
Solve the given system:
x'-4x+3y''=t^2 and x'+x+y'=0

x’+2x=sin(t), x(0)=1
solve the first order differential equation.

Use the Laplace Transform method to solve the following
differential equation problem: y 00(t) − y(t) = t + sin(t), y(0) =
0, y0 (0) = 1
Please show partial fraction steps to calculate
coeffiecients.

Solve the 2nd Order
Differential Equation using METHOD OF REDUCTION
Please don't skip
steps!
(x-1)y"-xy'+y=0 x>1
y1(x)=x
My professor is
getting y2(x)=e^x and I don't understand how!

Please show all steps, thanks!!
a) Solve the BVP: y" + 2y' + y = 0, y(0) = 1, y(1) =3
b) Prove the superposition principle: suppose that the functions
y1(x) and y2(x) satisfy the homogenous equation of order two: ay''
+ by' + cy = 0.
Show that the following combinations also satisfy it:
constant multiple m(x) = k*y1(x)
sum s(x) = y1(x) + y2(x)

Q8)Problem Kong1: Solve for the general solution of the
equation:
2x’’+ 200x = 0. Show all math steps.
Q9)Problem Kong2: Solve for the particular solution of Kong1 if
x(0)=1 and x’(0)=20. Show all math steps.
Q10)Problem Kong3: Solve for the general
solution of the equation: 2y’’ + 4y’ + 200y = 0. Show
all math steps.

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