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CALCULUS AND ANALYSIS
DIFFERENTIAL EQUATIONS
SECOND ORDER LINEAR EQUATIONS
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First order differential equations
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Second order linear equations
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Differential equations
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Second order linear equations Answers
Second order linear equations
asked 2021-03-11
Solve the linear equations by considering y as a function of x, that is, y = y(x).
\(y'+2y=4\)
Second order linear equations
asked 2021-03-07
Solve the correct answer linear equations by considering y as a function of x, that is,
\(\displaystyle{d}{i}{s}{p}{l}{a}{y}{s}{t}{y}\le{\left\lbrace{y}\right\rbrace}={\left\lbrace{y}\right\rbrace}{\left\lbrace{\left({\left\lbrace{x}\right\rbrace}\right)}\right\rbrace}.{\frac{{{\left\lbrace\le{f}{t}.{\left\lbrace{d}\right\rbrace}{\left\lbrace{y}\right\rbrace}{r}{i}{g}{h}{t}.\right\rbrace}}}{{{\left\lbrace\le{f}{t}.{\left\lbrace{d}\right\rbrace}{\left\lbrace{x}\right\rbrace}{r}{i}{g}{h}{t}.\right\rbrace}}}}+{\left\lbrace{y}\right\rbrace}={\cos{{\left\lbrace{\left\lbrace{x}\right\rbrace}\right\rbrace}}}\)
Second order linear equations
asked 2021-02-25
Solve the linear equations by considering y as a function of x, that is, y = y(x).
\(\displaystyle\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}-{y}={4}{e}^{x},{y}{\left({0}\right)}={4}\)
Second order linear equations
asked 2021-02-24
Solve the linear equations by considering y as a function of x, that is, y = y(x).
\(\displaystyle\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}+{\left(\frac{1}{{x}}\right)}{y}={x}\)
Second order linear equations
asked 2021-02-21
Linear equations of second order with constant coefficients.
Find all solutions on
\(\displaystyle{\left(-\infty,+\infty\right)}.{y}\text{}-{2}{y}'+{5}{y}={0}\)
Second order linear equations
asked 2021-02-16
A dynamic system is represented by a second order linear differential equation.
\(2\frac{d^2x}{dt^2}+5\frac{dx}{dt}-3x=0\)
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.
Second order linear equations
asked 2021-02-12
Contain linear equations with constants in denominators. Solve each equation
\(\displaystyle{d}{i}{s}{p}{l}{a}{y}{s}{t}{y}\le{\frac{{{\left\lbrace{\left\lbrace{5}\right\rbrace}+{\left\lbrace{x}\right\rbrace}-{\left\lbrace{2}\right\rbrace}\right\rbrace}}}{{{\left\lbrace{3}\right\rbrace}}}}={\frac{{{\left\lbrace{\left\lbrace{x}\right\rbrace}+{\left\lbrace{3}\right\rbrace}\right\rbrace}}}{{{\left\lbrace{8}\right\rbrace}}}}\)
Second order linear equations
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.
Second order linear equations
asked 2021-02-12
On solution of the differetial equation
\(y''+y'=0\)
is
\(y=e^{-x}\)
. Use Reduction of Order to find a second linearly independent solution.
Second order linear equations
asked 2021-02-12
Solve the linear equations by considering y as a function of x, that is,
\(y = y(x)\)
\(3xy'+y=12x\)
Second order linear equations
asked 2021-02-09
Solve the following non-homogeneous second order linear differential equation.
\(y''+py'-qy=-rt\)
if
\(p=4,\ q=8,\ r=7\)
.
Second order linear equations
asked 2021-02-06
Solve the differential equation:
\(y''+6y'+12y=0\)
Second order linear equations
asked 2021-02-05
A differential equation and a nontrivial solution f are given below. Find a second linearly independent solution using reduction of order. Assume that all constants of integration are zero.
\(tx''-(2t+1)x+2x=0,\ t>0,\ f(t)=3*e^{2t}\)
Second order linear equations
asked 2021-02-02
Find the general solution of the second order non-homogeneous linear equation:
\(y''-7y'+12y=10\sin t+12t+5\)
Second order linear equations
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.
Second order linear equations
asked 2021-01-27
Cosider the system of differential equations
\(x_1'=2x_1+x_2\)
\(x_2'=4x_1-x_2\)
Convert this system to a second order differential equations and solve this second order differential equations
Second order linear equations
asked 2021-01-13
Solve the linear equations by considering y as a function of x, that is, y = y(x).
\displaystyle{y}'+{y} \tan{{x}}= \sec{{x}},\)
\displaystyle{y}{\left(\pi\right)}={1}\)
Second order linear equations
asked 2021-01-10
Solve the following IVP for the second order linear equations
\(y''-4y'+9y=0,\ \ y(0)=0,\ \ y'(0)=-8\)
Second order linear equations
asked 2021-01-10
Using the existence and uniqueness theorem for second order linear ordinary differential equations, find the largest interval in which the solution to the initial value is certain to exist.
\(t(t^2-4)y''-ty'+3t^2y=0, y(1)=1 y'(1)=3\)
Second order linear equations
asked 2021-01-08
Give the correct answer and solve the given equation
\(xy′′ − y′ = (3 + x)x^{2}e^{x}\)
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