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

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Algebraic!Best ResponseYou've already chosen the best response.1
did you get that problem from the other day sorted out?
 one year ago

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

MathSofiyaBest ResponseYou've already chosen the best response.0
but that is apparently wrong
 one year ago

MathSofiyaBest ResponseYou've already chosen the best response.0
iirc? what does that mean?
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
if I recall correctly
 one year ago

MathSofiyaBest ResponseYou've already chosen the best response.0
\[y_c=c_1cosx+c_2sinx\]
 one year ago

MathSofiyaBest ResponseYou've already chosen the best response.0
\[W(y_1,y_2)=cos^2x+sin^2x\]
 one year ago

MathSofiyaBest ResponseYou've already chosen the best response.0
nice! \[y_p=cosx\int sinxsec^2xdx+sinx \int cosxsec^2xdx\]
 one year ago

MathSofiyaBest ResponseYou've already chosen the best response.0
\[y=y_c+y_p=c_1cosx+c_2sinxcosxsecx+\int cosxsec^2xdx\]
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
missing a 'sin' on that last term...
 one year ago

psi9epsilonBest ResponseYou've already chosen the best response.0
@mathsofiya , check integration seems incomplete
 one year ago

psi9epsilonBest ResponseYou've already chosen the best response.0
@Algebraic! , didnt really see the reason for "lol", there are couple of things missing here
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
"integration seems incomplete"
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
what tipped you off?
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
here I thought you were making a funny and you were somehow serious...
 one year ago

psi9epsilonBest 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 : )
 one year ago

MathSofiyaBest ResponseYou've already chosen the best response.0
where's a sine missing?
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
sinx∫cosxsec^2x dx > ∫cosxsec^2x dx
 one year ago

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

MathSofiyaBest 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
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
most people use ln(tan(x) +sec(x)) for brevity
 one year ago

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