Question

Find the general solution of the given differential equation.

y'' + 12y' + 85y = 0

y(t) =

Answer #1

Given question solved.

a) Find the general solution of the differential equation
y''-2y'+y=0
b) Use the method of variation of parameters to find the general
solution of the differential equation y''-2y'+y=2e^t/t^3

Find the general solution of the given differential
equation.
y'' − y' − 2y = −8t + 6t2
y(t) =

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)

(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

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 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 of the differential equation
y′′+9y=11sec2(3t), 0<t<π6.

Use variation of parameters to find a general solution to the
differential equation given that the functions y1 and y2 are
linearly independent solutions to the corresponding homogeneous
equation for t>0.
y1=et y2=t+1
ty''-(t+1)y'+y=2t2

find the general solution of the given differential
equation:
4y′′−4y′+y=16e^t/2

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

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