Question

find the general solution.

1- y^6(4)+12y''+36y=0

2-6y^(4)+5y'''+7y''+5y'+y=0

3-y^(4)-4y'''+7y''-6y'+2y=0

Answer #1

find the solution:
y'''+2y''-5y'-6y=7t²
y(0)=1, y'(0)=3, y''(0)=-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

Find the general solution to y'' + 7y' + 12y = x + 1.

(a) Solve the differential equations.
4y´´ + 12y´ + 9y= 0
(b) Find the general solution of the ODE
y´´- 5y´+4y=e^4t
(c) Solve the following initial value problem:
y´´+ y =0, y(0)=2, y´(0)=2

Question : y''+6y'+9y=0,y(0)=2,y'(0)=1 ,
4y''+12y'+9y=0,y(0)=2,y'(0)=2
y''-y'-2y=cosx , y''+3y'+2y=x^2 - e^2x ,
y''-3y'+2y=sinx , y''-2y'-3y=3e^2x

Non homogeneous eq w constant; undetermined coefficients
Find the general solution:
1) y" + 4y' + 4y = xe^−x.
2) y" + 2y' + 5y = e^2x cos x.
Determine a suitable form for a particular solution z = z(x) of
the given equations
1) y" + 2y' = 2x + x^2e^−3x + sin 2x.
2) y" − 5y' + 6y = 2e^2x cos x − 3xe^3x + 5.
3) y" + 5y' + 6y = 2e^2x cos x −...

Question 4
a) Solve y```` -4y```-5y``+36Y`− 36?=0 knowing that xe^2x it's a
solution
b) Determine the general solution for a linear homogeneous
differential equation in y(x) de fourth order, with real
coefficients, knowing that a solution is given by x^3e^4x.
Leave the calculations recorded in the
activity

Find the solution of the given initial value problems.
6y"-5y'+y=0, y(0)=4 , y'(0)=0

1. Find the general solution of each of the following
differential equations a.) y' − 4y = e^(2x) b.) dy/dx = 1/[x(y −
1)] c.) 2y'' − 5y' − 3y = 0

Find the general solution of the equation: y''+6y'+9y=0 where
y(1)=3 y' (1)=-2 and then find the particular solution.

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