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sjerman1
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differential equations > xe^t dx/dt=t with the initial condition that x(0) = 1.
 one year ago
 one year ago
sjerman1 Group Title
differential equations > xe^t dx/dt=t with the initial condition that x(0) = 1.
 one year ago
 one year ago

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sjerman1 Group TitleBest ResponseYou've already chosen the best response.0
\[xe ^{t} \frac{ dx }{ dt }=t\]
 one year ago

sjerman1 Group TitleBest ResponseYou've already chosen the best response.0
\[\int\limits x dx=\int\limits \frac{ t }{ e^{t}} dt \]
 one year ago

sjerman1 Group TitleBest ResponseYou've already chosen the best response.0
is where im at now, wondering if this is correct
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
\[\large \int\limits\limits x dx=\int\limits\limits t e^t\; dt\] Yup looks good so far. By Parts on the right side :D
 one year ago

sjerman1 Group TitleBest ResponseYou've already chosen the best response.0
\[\frac{ x^2 }{ 2 }+c=e^t(t1)\]
 one year ago

sjerman1 Group TitleBest ResponseYou've already chosen the best response.0
right o got that now solving for c hold on
 one year ago

sjerman1 Group TitleBest ResponseYou've already chosen the best response.0
\[\frac{ 1 }{ 2 }+c=e^0(01)\] c=\[\frac{ 3 }{ 2 }\]
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
yay good job c: Pshhhh you didn't need any help with this one lol
 one year ago

sjerman1 Group TitleBest ResponseYou've already chosen the best response.0
so now i have \[\frac{ x^2 }{ 2 }\frac{ 3 }{ 2 }=e^t(t1)\]
 one year ago

sjerman1 Group TitleBest ResponseYou've already chosen the best response.0
now the hard part for me is solving for x because the answer wants it in x= soooo what can i do to the 3/2? would that be added to the 1? so the right side would be e^t(t+1/2)?
 one year ago

sjerman1 Group TitleBest ResponseYou've already chosen the best response.0
\[\frac{ x^2 }{ 2 }=e^t(t1)+\frac{ 3 }{ 2 }\]
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
Multiply both sides by 2\[\large x^23=2e^t(t1)\]Add 3 to both sides,\[\large x^2=2e^t(t1)+3\]Square root,\[\large x=\pm \sqrt{2e^t(t1)+3}\]
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
That's probably the route I would take. Get rid of the ugly fraction first :D
 one year ago

sjerman1 Group TitleBest ResponseYou've already chosen the best response.0
ohhhh my that is what i was going to ask next. but multiplying by two is probaly the rout my prof would have taken. Thank you @zepdrix !
 one year ago
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