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HallsofIvy
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Today,
00:19
MarkFL
replied to a thread
1.3.14 Verify the following given functions is a solution
in
Differential Equations
You are given $y$, and from this you need to compute $y'$, so you can then substitute both into the given ODE and see if an identity results. Also,...
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1 replies | 17 view(s)
June 22nd, 2018,
21:15
MarkFL
replied to a thread
1.1.2 de solution?
in
Differential Equations
I asked it a total of 3 times. You kept ignoring me for some reason.
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12 replies | 133 view(s)
June 22nd, 2018,
19:06
MarkFL
replied to a thread
1.1.2 de solution?
in
Differential Equations
I guess this question has gotten lost in all the excitement the first two times I asked it? Hopefully it is visible now. (Giggle)
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12 replies | 133 view(s)
June 22nd, 2018,
13:28
MarkFL
replied to a thread
1.1.2 de solution?
in
Differential Equations
You can do the differentiation on the exponential definition of the function... \cosh(x)=\frac{1}{2}\left(e^x+e^{-x}\right) What about $y_3$?
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12 replies | 133 view(s)
June 22nd, 2018,
04:53
MarkFL
replied to a thread
1.1.2 de solution?
in
Differential Equations
Recall: \cosh(x)\equiv\frac{e^x+e^{-x}}{2} How about: y_3(x)=c_1e^x+c_2e^{-x} ?
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12 replies | 133 view(s)
June 22nd, 2018,
03:54
MarkFL
replied to a thread
1.1.2 de solution?
in
Differential Equations
Yes: \frac{d^2}{dx^2}\left(e^x\right)=e^x What about the hyperbolic cosine function $y_2(x)$ ?
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12 replies | 133 view(s)
June 22nd, 2018,
02:20
MarkFL
replied to a thread
1.1.2 de solution?
in
Differential Equations
You want to see if: y_n''-y_n=0 where n\in\{1,2\} In other words, are the given functions equal to their own second derivative?
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12 replies | 133 view(s)
June 21st, 2018,
00:02
MarkFL
replied to a thread
2.2.8 de xy'+2y=sin x,y(pi)=1/pi find solution
in
Differential Equations
You wound up with $x^2\sin(x)$ on the RHS before integrating, but it should be $x\sin(x)$. :)
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2 replies | 76 view(s)
June 20th, 2018,
19:23
MarkFL
replied to a thread [SOLVED]
2.2.7 de with trig and y(1)=1
in
Differential Equations
When you multiply through by $\mu(x)$, you should have: \frac{d}{dx}(\sin(x)y)=2 And then integrate: \sin(x)y=2x+c_1 ...
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2 replies | 43 view(s)
June 19th, 2018,
19:21
MarkFL
replied to a thread
2.2.6 de with e^x
in
Differential Equations
Towards the end, when you divide through by $x$, you want: y(x)=\frac{e^x}{x}+\frac{c}{x} You mistakenly divided the constant by $e^x$.
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1 replies | 45 view(s)
June 19th, 2018,
15:31
MarkFL
replied to a thread
2.2.5 de equation with y(1)=1/2
in
Differential Equations
Yes, but you used it on the original ODE, not the one in standard linear form. :)
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4 replies | 106 view(s)
June 17th, 2018,
12:39
MarkFL
replied to a thread [SOLVED]
2.2.3 de with tan x
in
Differential Equations
I can't imagine trying to use the internet on a telephone. I'm sorry scrolling on a telephone is such a chore...they should fix that.
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8 replies | 115 view(s)
June 17th, 2018,
00:59
MarkFL
replied to a thread [SOLVED]
2.2.3 de with tan x
in
Differential Equations
Are you using Tapatalk by any chance? I have code in place to let me know when posts have been edited, so I don't miss added content (it's better to...
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8 replies | 115 view(s)
June 17th, 2018,
00:52
MarkFL
replied to a thread [SOLVED]
2.2.3 de with tan x
in
Differential Equations
When you multiply by $\mu(x)$, you get: \sec(x)y'+\tan(x)\sex(x)y=\sec(x)\sin(2x) This can be written as: ...
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8 replies | 115 view(s)
June 16th, 2018,
19:51
MarkFL
replied to a thread [SOLVED]
2.2.3 de with tan x
in
Differential Equations
-\ln(\cos(x))=\ln\left((\cos(x))^{-1}\right)=\ln(\sec(x))
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8 replies | 115 view(s)
June 16th, 2018,
19:38
MarkFL
replied to a thread [SOLVED]
2.2.3 de with tan x
in
Differential Equations
\mu(x)=\exp\left(\int \tan(x)\,dx\right)=e^{\Large\ln(\sec(x))}=\sec(x)
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8 replies | 115 view(s)
June 16th, 2018,
00:29
MarkFL
replied to a thread
Problems with Percentage
in
Pre-Algebra and Algebra
300+300\cdot\frac{1666}{100}=300(1+16.66)=300\cdot17.66=5298 Here, we have taken 300, and added 1666% of 300 to it. However if we multiply 300 by...
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6 replies | 144 view(s)
June 15th, 2018,
16:28
MarkFL
replied to a thread [SOLVED]
2.2.1 de with u substitution
in
Differential Equations
\mu(x)=\exp\left(\int\frac{1}{x}\,dx\right)=e^{\ln(x)}=x
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3 replies | 65 view(s)
June 15th, 2018,
15:53
MarkFL
replied to a thread [SOLVED]
2.2.1 de with u substitution
in
Differential Equations
We can see the integrating factor is $\mu(x)=x$ and so the ODE will become: \frac{d}{dx}(xy)=x\sin(x) Upon integrating, we get: ...
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3 replies | 65 view(s)
June 15th, 2018,
14:14
MarkFL
replied to a thread
2.1.9 de with reciprocal
in
Differential Equations
That's fine giving $x$ as a function of $y$...I just chose to give $y$ as a function of $x$ since the original equation has $x$ as the independent...
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4 replies | 74 view(s)
June 15th, 2018,
12:44
MarkFL
replied to a thread
2.1.9 de with reciprocal
in
Differential Equations
We could also simply state: \d{x}{y}=e^y-x \d{x}{y}+x=e^y Now, our integrating factor is: \mu(y)=\exp\left(\int\,dy\right)=e^y
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4 replies | 74 view(s)
June 15th, 2018,
03:08
MarkFL
replied to a thread
2.1.9 de with reciprocal
in
Differential Equations
I would begin here with the substitution: u=e^y\implies u'=uy' And so the ODE becomes: \frac{1}{u}u'=\frac{1}{u-x} Or:
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4 replies | 74 view(s)
June 14th, 2018,
11:23
MarkFL
replied to a thread
Rationalize expression
in
Pre-Algebra and Algebra
Hello and welcome to MHB! (Wave) I've moved this thread to our elementary algebra forum, since this is a better fit for the problem and I've give...
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2 replies | 99 view(s)
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