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POST SECONDARY
CALCULUS AND ANALYSIS
DIFFERENTIAL EQUATIONS
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Recent Differential equations Answers
Recent questions in Differential equations
Differential equations
asked 2020-11-12
\(F(x) = (lnx)^{\cos}x,\)
find f'(x) and the equation to the tangent line at (e 1)
First order differential equations
asked 2020-11-10
Solve differential equation
\(\displaystyle{y}'+{y}{\cot{{\left({x}\right)}}}={\sin{{\left({2}{x}\right)}}}\)
Laplace transform
asked 2020-11-10
Solve by Laplace transforms
\(y"-3y'+2y=2\delta(t-1)\)
\(y(0)=1\)
\(y'(0)=0\)
Laplace transform
asked 2020-11-10
use the Laplace transform to solve the given initial-value problem.
\(y"-3y'+2y=4 \ , \ y(0)=0 \ , \ y'(0)=1\)
First order differential equations
asked 2020-11-10
Find the sokaton 02 the ger Initial value provsem.
\(y′−y=8t2,y(0)=1\)
First order differential equations
asked 2020-11-10
Solve differential equation
\((2y-e^x)dx+xdy=0\)
, x>0
Differential equations
asked 2020-11-09
solve the Differential equations
\(\displaystyle{y}{'''}+{10}{y}{''}+{25}{y}'={0}\)
Second order linear equations
asked 2020-11-09
Solve for the general solution of the given special second-ordered differential equation
\(xy''+x(y')^2-y'=0\)
Second order linear equations
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
\(y_2\)
.
Laplace transform
asked 2020-11-09
Find x(t) and Y(t) using Laplace transform.
\(\begin{cases} \frac{dx}{dt}=2x-3y
\frac{dy}{dt}=y-2x \end{cases}\)
\(x(0)=8 , y(0)=3\)
Laplace transform
asked 2020-11-09
determine the inverse Laplace transform of the function.
\(\displaystyle{Q}{\left({s}\right)}=\frac{s}{{{s}^{2}+{64}}}\)
Laplace transform
asked 2020-11-09
Use Laplace transform to evaluate the integral
\(\int_0^\infty te^{-2t} \sin(2t)dt\)
a)
\(\frac{1}{B}\)
b) not defined
c)
\(\frac{4s}{(s^2+4)^2}\)
d)
\(\frac{4(s+2)}{(s^2+4s+8)^2}\)
Laplace transform
asked 2020-11-09
Solve the third-order initial value problem below using the method of Laplace transforms
\(y'''-2y"-21y'-18y=-18\)
\(y(0)=2\)
\(y'(0)=7\)
\(y"(0)=95\)
Laplace transform
asked 2020-11-09
Solve the inital value problem by using Laplace transform:
\(y''-5y'+6y=-8\cos(t)-2\sin(t), y(\frac{\pi}{2})=1 ,y'(\frac{\pi}{2})=0\)
First order differential equations
asked 2020-11-09
Solve differential equation
\(xy'= 6y+12x^4 y^(2/3)\)
Differential equations
asked 2020-11-08
A particle moves along the curve
\(\displaystyle{x}={2}{t}^{{2}}{y}={t}^{{2}}-{4}{t}\)
and z=3t-5 where t is the time.find the components of the velocity at t=1 in the direction i-3j+2k
Laplace transform
asked 2020-11-08
How to solve this equation
\(y'''-4y"+2y'-16y=4x+1\)
using Method of Undetermined Coefficient, Variation of Parameters and Laplace Transformation
Laplace transform
asked 2020-11-08
Given that
\(f{{\left({t}\right)}}={4}{e}^{{-{3}{\left({t}-{4}\right)}}}\)
a) Find
\({L}{\left[\frac{{{d} f{{\left({t}\right)}}}}{{{\left.{d}{t}\right.}}}\right]}\)
by differentiating f(t) and then using the Laplace transform tables in lecture notes.
b) Find
\({L}{\left[\frac{{{d} f{{\left({t}\right)}}}}{{{\left.{d}{t}\right.}}}\right]}\)
using the theorem for differentiation
c) Repeat a) and b) for the case that
\(f{{\left({t}\right)}}={4}{e}^{{-{3}{\left({t}-{4}\right)}}}{u}{\left({t}-{4}\right)}\)
Laplace transform
asked 2020-11-08
Given the function
\(\begin{cases}e^{-t}& \text{if } 0\leq t<2\\ 0&\text{if } 2\leq t\end{cases}\)
Express f(t) in terms of the shifted unit step function u(t -a)
F(t) - ?
Now find the Laplace transform F(s) of f(t)
F(s) - ?
Laplace transform
asked 2020-11-08
Find the solution of the Differentional equation by using Laplace Transformation
\(2y'-3y=e^{2t}, y(0)=1\)
\(y"+y=t, y(0)=0 and y'(0)=2\)
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