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POST SECONDARY
CALCULUS AND ANALYSIS
INTEGRAL CALCULUS
DIFFERENTIAL EQUATIONS
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Differential equations answers
Recent questions in Differential equations
meplasemamiuk
2021-11-11
Answered
Find the general solution of the given differential equation.
\(\displaystyle{y}^{{{\left({6}\right)}}}-{y}{''}={0}\)
jernplate8
2021-11-10
Answered
Write the formula for the derivative of the function.
\(\displaystyle{f{{\left({x}\right)}}}={12}{x}^{{{4}}}+{19}{x}^{{{3}}}+{9}\)
f'(x)=
Emily-Jane Bray
2021-11-09
Answered
Write the formula for the derivative of the function.
\(\displaystyle{g{{\left({x}\right)}}}=-{3.1}{x}^{{{3}}}+{6.1}{x}-{6.6}\)
g'(x)=
ankarskogC
2021-11-05
Answered
Find the general solution for the following differential equation.
\(\displaystyle{\frac{{{d}^{{{3}}}{y}}}{{{\left.{d}{x}\right.}^{{{3}}}}}}-{\frac{{{d}^{{{2}}}{y}}}{{{\left.{d}{x}\right.}^{{{2}}}}}}-{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}+{y}={x}+{e}^{{-{x}}}\)
.
Tahmid Knox
2021-10-23
Answered
Show that any separable equation
\(\displaystyle{M}{\left({x},{y}\right)}+{N}{\left({x},{y}\right)}{y}'={0}\)
facas9
2021-10-21
Answered
Find the solution of the given initial value problem.
\(\displaystyle{y}'−{2}{y}={e}{2}{t},{y}{\left({0}\right)}={2}\)
slaggingV
2021-10-21
Answered
Find the differntial of each function.
a)
\(\displaystyle{y}={\tan{\sqrt{{{7}{t}}}}}\)
b)
\(\displaystyle{y}={\frac{{{3}-{v}^{{2}}}}{{{3}+{v}^{{2}}}}}\)
Marvin Mccormick
2021-10-21
Answered
Differentiate.
\(\displaystyle{H}{\left({u}\right)}={\left({u}-\sqrt{{{u}}}\right)}{\left({u}+\sqrt{{{u}}}\right)}\)
tabita57i
2021-10-19
Answered
Find
\(\displaystyle{\frac{{{\left.{d}{z}\right.}}}{{{\left.{d}{x}\right.}}}}\)
and
\(\displaystyle{\frac{{{\left.{d}{z}\right.}}}{{{\left.{d}{y}\right.}}}}\)
.
\(\displaystyle{z}={\frac{{{x}{y}}}{{{x}^{{2}}+{y}^{{2}}}}}\)
FizeauV
2021-10-18
Answered
Find the general solution of the given differential equation.y” + 2y' + y = 2e−t
illusiia
2021-10-17
Answered
Find r(t) if
\(\displaystyle{r}'{\left({t}\right)}={t}{i}+{e}^{{t}}{j}+{t}{e}^{{k}}\)
and
\(\displaystyle{r}{\left({0}\right)}={i}+{j}+{k}\)
ediculeN
2021-10-17
Answered
A part icle moves along the curve
\(\displaystyle{y}={2}{\sin{{\left(\pi\frac{{x}}{{2}}\right)}}}\)
. As the particle passes through the point
\(\displaystyle{\left(\frac{{1}}{{3}},{1}\right)}\)
its x-coordinate increases at a rate of
\(\displaystyle\sqrt{{{10}}}\)
cm/s. How fast is the distance from the particle to the origin changing at this instant?
cistG
2021-10-15
Answered
A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat. If the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching the dock when it is 8 m from the dock?
FobelloE
2021-10-14
Answered
Determine whether the given differential equation is exact. If it is exact, solve it.
\(\displaystyle{\left({x}-{y}^{{3}}+{y}^{{2}}{\sin{{x}}}\right)}{\left.{d}{x}\right.}={\left({3}{x}{y}^{{2}}+{2}{y}{\cos{{x}}}\right)}{\left.{d}{y}\right.}\)
Anonym
2021-10-12
Answered
Solve the given differential equation by separation of variables.
\(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\left({x}+{1}\right)}^{{{2}}}\)
Nannie Mack
2021-10-12
Answered
Solve the initial value problem for
r
as a vector function of t. Differential equation:
\(\displaystyle{\frac{{{d}{r}}}{{{\left.{d}{t}\right.}}}}=-{t}{i}-{t}{j}-{t}{k}\)
Initial condition:
r(0)=i+2j+3k
Caelan
2021-10-09
Answered
Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
\(\displaystyle{y}{\sin{{\left({12}{x}\right)}}}={x}{\cos{{\left({2}{y}\right)}}},{\left(\frac{\pi}{{2}},\frac{\pi}{{4}}\right)}\)
Harlen Pritchard
2021-10-09
Answered
Use implicit differentiation to find
\(\displaystyle{\frac{{{\left.{d}{z}\right.}}}{{{\left.{d}{x}\right.}}}}\)
and
\(\displaystyle{\frac{{{\left.{d}{z}\right.}}}{{{\left.{d}{y}\right.}}}}\)
\(\displaystyle{e}^{{z}}={x}{y}{z}\)
opatovaL
2021-10-08
Answered
Solve the given differential equation by separation of variables.
\(\displaystyle{\frac{{{d}{P}}}{{{\left.{d}{t}\right.}}}}={P}-{P}^{{2}}\)
necessaryh
2021-10-05
Answered
Consider the system of differential equations
\(\displaystyle{\frac{{{\left.{d}{x}\right.}}}{{{\left.{d}{t}\right.}}}}=-{y}\ \ \ {\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{t}\right.}}}}=-{x}\)
.a)Convert this system to a second order differential equation in y by differentiating the second equation with respect to t and substituting for x from the first equation.
b)Solve the equation you obtained for y as a function of t; hence find x as a function of t.
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