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MathSofiya
Group Title
solve the differential equation using the variation of parameters method
\[y''+y=sec^2x,0\le x\le \frac{\pi}2\]
\[r^2+1=0\]
 2 years ago
 2 years ago
MathSofiya Group Title
solve the differential equation using the variation of parameters method \[y''+y=sec^2x,0\le x\le \frac{\pi}2\] \[r^2+1=0\]
 2 years ago
 2 years ago

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Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
did you get that problem from the other day sorted out?
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
y" +y =t*e^t iirc?
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.0
at first I had r^2+r=0 and that gave me the integral of \[\int\frac{e^{x}sec^2x}{e^{x}}dx+e^{x}\int \frac{sec^2x}{e^{x}}dx\]
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.0
but that is apparently wrong
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.0
iirc? what does that mean?
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
if I recall correctly
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.0
\[r_1=r_2=\pm1i\]
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.0
\[y_c=c_1cosx+c_2sinx\]
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.0
\[W(y_1,y_2)=cos^2x+sin^2x\]
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.0
nice! \[y_p=cosx\int sinxsec^2xdx+sinx \int cosxsec^2xdx\]
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.0
so far so good?
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.0
\[y=y_c+y_p=c_1cosx+c_2sinxcosxsecx+\int cosxsec^2xdx\]
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
missing a 'sin' on that last term...
 2 years ago

psi9epsilon Group TitleBest ResponseYou've already chosen the best response.0
@mathsofiya , check integration seems incomplete
 2 years ago

psi9epsilon Group TitleBest ResponseYou've already chosen the best response.0
@Algebraic! , didnt really see the reason for "lol", there are couple of things missing here
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
"integration seems incomplete"
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
what tipped you off?
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
here I thought you were making a funny and you were somehow serious...
 2 years ago

psi9epsilon Group TitleBest ResponseYou've already chosen the best response.0
a simple look suggests that last term carries an Integration sign whereas the second last term does not, it cant be both , either we have an integral sign or we dont. Anyways its better to teach something correctly : )
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.0
where's a sine missing?
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
sinx∫cosxsec^2x dx > ∫cosxsec^2x dx
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.0
very true \[y=y_c+y_p=c_1cosx+c_2sinxcosxsecx+sinx\int cosxsec^2xdx\]
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.0
is this really the solution to the integral? http://www.wolframalpha.com/input/?i=integral+of+cosxsec^2x
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
most people use ln(tan(x) +sec(x)) for brevity
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
programs always give the other form of the answer; not sure why, probably to confound students.
 2 years ago
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