Question

Prove the equation is solution of the given differential equation.

**1.) y= 5sin5x+5cos5x**

**y"+25y=0**

Answer #1

ﬁnd the general solution of the given differential equation
1. y''−2y'+2y=0
2. y''+6y'+13y=0
ﬁnd the solution of the given initial value problem
1. y''+4y=0, y(0) =0, y'(0) =1
2. y''−2y'+5y=0, y(π/2) =0, y'(π/2) =2
use the method of reduction of order to ﬁnd a second solution of
the given differential equation.
1. t^2 y''+3ty'+y=0, t > 0; y1(t) =t^−1

<question 1>
find a solution for the given differential equation. if
possible, find a particular solution byspecifying the integral
coefficient. please show details of your work.
1) y'+(x^2)y=(e^(-x^3)sinhx)/3y^3
(hint : integral of sinh is cosh : you can prove this by using
the definition of cosh and sinh)
2) y''+2y'+y=2xsinx
3) y''+10y'+25y=100sinh(5x)
(hint : sin(5x)=1/2(e^5x-e^(-5x))

Find the general solution of the given differential
equation.
y'' + 12y' + 85y = 0
y(t) =

given the differential equation y'+y=x^2+2x, compute the value of
the solution y(x) at x=1 given the inital condition y(0)=2. Also,
use h=0.1

Find
a) the general solution of the differential equation y' = ( y^2
+ 1 ) ( 2x + 3)
b ) if the particular solution (if it exists) of the above
mentioned differential equation that satisfies the initial
condition y(0) = -1

Find the general solution to the differential equation: y’’ – 6
y’ + 13y = 0
Find the general solution to the differential equation: y’’ +
5y’ + 4y = x + cos(x)

26. Find the solution of the differential equation.
y'' +4y' +4y =0 ; y(-1)=2 and y'(-1)=-1

Given the differential equation to the right y''-3y'+2y=0
a) State the auxiliary equation.
b) State the general solution.
c) Find the solution given the following initial conditions
y(0)=4 and y'(0)=5

Differential Equations problem
If y1= e^-x is a solution of the differential equation
y'''-y''+2y=0 . What is the general solution of the differential
equation?

1) find a solution for a given differential equation
y1'=3y1-4y2+20cost ->y1 is not y*1 & y2 is not y*2
y2'=y1-2y2
y1(0)=0,y2(0)=8
2)by setting y1=(theta) and y2=y1', convert the following 2nd
order differential equation into a first order system of
differential equations(y'=Ay+g)
(theta)''+4(theta)'+10(theta)=0

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 7 minutes ago

asked 17 minutes ago

asked 18 minutes ago

asked 21 minutes ago

asked 34 minutes ago

asked 44 minutes ago

asked 49 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago