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

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

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

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

zepdrix
 one year ago
Best 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

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

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

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

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

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

sjerman1
 one year ago
Best ResponseYou've already chosen the best response.0now 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)?

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

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

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

sjerman1
 one year ago
Best ResponseYou've already chosen the best response.0ohhhh 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 !
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