Solve the differential equation: y''+6y'+12y=0

Solve the differential equation:

Answers (1)

Given the Differential Equation is
This is a second-order linear differential equation with constant coefficients
Auxilary Equation is
Solve This quadratic equation.
Compare with:
So roots are
\(a=1,\ b=6,\ c=12\)
So here Roots of equations are complex
So Solution of Ordinary differential equation with root a+ib and a-ib is
Here \(a=-3\) and \(b=\sqrt3\)
So the solution is

Relevant Questions

asked 2021-02-12
\(y=3e^{3x}\) is a solution of a second order linear homogeneous differential equation with constant coefficients. The equation is:
(a) \(y''-(3+a)y'+3ay=0\), a any real number.
(b) \(y''+y'-6y=0\)
(c) \(y''+3y'=0\)
(d) \(y''+(3-a)y'+3ay=0\), a any real number.
(e) Cannot be determined.
asked 2020-11-09
Solve for the general solution of the given special second-ordered differential equation
asked 2021-02-02
Find the general solution of the second order non-homogeneous linear equation:
\(y''-7y'+12y=10\sin t+12t+5\)
asked 2021-02-09
Solve the following non-homogeneous second order linear differential equation.
if \(p=4,\ q=8,\ r=7\).
asked 2020-12-07
Solve the second order linear differential equation using method of undetermined coefficients
asked 2021-02-16
A dynamic system is represented by a second order linear differential equation.
The initial conditions are given as:
when \(t=0,\ x=4\) and \(\frac{dx}{dt}=9\)
Solve the differential equation and obtain the output of the system x(t) as afunction of t.
asked 2020-11-09
Let \(y_1\) and \(y_2\) be solution of a second order homogeneous linear differential equation \(y''+p(x)y'+q(x)=0\), in R. Suppose that \(y_1(x)+y_2(x)=e^{-x}\),
\(W[y_1(x),y_2(x)]=e^x\), where \(W[y_1,y_2]\) is the Wro
ian of \(y_1\) and \(y_2\).
Find p(x), q(x) and the general form of \(y_1\) and \(y_2\).
asked 2021-01-28
One solution of the differential equation \(y" – 4y = 0\) is \(y = e^{2x} Find a second linearly independent solution using reduction of order.
asked 2020-11-02
Solve the Differential equations \(2y′′ + 3y′ − 2y = 14x^{2} − 4x − 11, y(0) = 0, y′(0) = 0\)
asked 2021-01-04
Verify that the given functions form a basis of solutions of the given equation and solve the given initial value problem.
\(4x^2-3y=0,\ y(1)=3,\ y'(1)=2.5,\) the basis of solution are \(y_1=x^{-\frac{1}{2}}\) and \(y_2=x(\frac{3}{2})\)