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Solve: $(x+1)^3y''+3(x+1)^2y'+(x+1)y=6\log(x+1)$
Solve: $(x+1)^3y''+3(x+1)^2y'+(x+1)y=6\log(x+1)$ Is my solution correct: Answer given in the book : $y(x+1)=c_1+c_2\log(x+1)+\log3(x+1)$ Fo...
Apr 17, 2026
Archive: News
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Velocity as a function of position, given velocity as a function of time
Knowing the expression for the acceleration as a function of time: $$ \frac{dv}{dt} = - c v^n$$ (for some constant c >0 and n >1), one needs to find...
Apr 17, 2026
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Symmetric property of a binary relation
A binary relation $\mathcal R$ on $E$ with graph $G$ is symmetric if and only if $\forall(x,y)\in E^2,\,x\mathcal R y\implies y\mathcal R x$. Suppose that...
Apr 17, 2026
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Given a Householder transformation
I am trying to solve a problem which is associated with Householder transformation. I know that given an unit complex vector $v$, I can get a Householder ...
Apr 17, 2026
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Maclaurin polynomial estimating $\sin 15°$
I would like to know how I would determine the Maclaurin polynomial which will estimate $\sin15°$ with an error less than $10^{-4}$. Maybe we have to use ...
Apr 17, 2026
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Related Rates Calculus - Confused About What dx/dt, dy/dt and dx/dy mean
Hello, I am confused as to how they got 5y in this problem when they multiplied dx/dy by dy/dt in the fourth line. I am also confused as to what dx/dt and...
Apr 17, 2026
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Find the area of a region using Green's Theorem.
Let $R$ be the region enclosed by the curve parameterized by $g(t) = (t^4 - t^2, t^6 - t^2)$, where $0 \leq t \leq 1.$ Find the area of $R$ using Green�...
Apr 17, 2026
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Finding the Zeros of A Function
In my Algebra II class we are learning how to find the zeros of a function, but I find the process very confusing despite the many efforts of my algebra t...
Apr 17, 2026
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Difference between pairwise distinct and unique?
I've come across the term "pairwise distinct" in many research papers. But, I don't understand how it differs from just saying that the elements...
Apr 17, 2026
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Name for a set which has an order?
As we all know, a set is a collection of elements which have no particular order and no multiplicity. So what do you call a construct which does store its...
Apr 17, 2026
