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ksaimouliBest ResponseYou've already chosen the best response.0
\[\frac{ dy }{ dx }=6x^2x^2y\]
 one year ago

SpacelimbusBest ResponseYou've already chosen the best response.1
\[\Large \frac{dy}{dx}=(6y)x^2 \] Or \[ \Large \frac{1}{6y}dy=x^2dx \] For \(y(x) \neq 6\)
 one year ago

ksaimouliBest ResponseYou've already chosen the best response.0
\[\int\limits_{}^{}\frac{ 1 }{ 6y }dy=x^2dx\]
 one year ago

SpacelimbusBest ResponseYou've already chosen the best response.1
Integrate both sides.
 one year ago

SpacelimbusBest ResponseYou've already chosen the best response.1
\[\Large  \ln 6y(x)=\frac{1}{3}x^3+C\prime \]
 one year ago

ksaimouliBest ResponseYou've already chosen the best response.0
they have given f(1)=2
 one year ago

SpacelimbusBest ResponseYou've already chosen the best response.1
You know you have to solve it for y(x) if you can, of course  you could apply the initial conditions just now and solve for the constant. But I strongly recommend you to get the equation in explicit form if possible.
 one year ago

ksaimouliBest ResponseYou've already chosen the best response.0
i got \[y(x)=ce ^{(x^3/x)}+6\]
 one year ago

SpacelimbusBest ResponseYou've already chosen the best response.1
Almost, try again. You should end up with: \[\Large y(x)=6Ce^{\frac{1}{3}x^3} \] As you can see, I said above that \(y(x) \neq 6\) which was important, otherwise I would have divided the differential equation through 0. This equation supports that statement, this equation only becomes 6 in the limit as x approaches infinity.
 one year ago

ksaimouliBest ResponseYou've already chosen the best response.0
dw:1360441531205:dw
 one year ago

ksaimouliBest ResponseYou've already chosen the best response.0
dw:1360441583641:dw
 one year ago

SpacelimbusBest ResponseYou've already chosen the best response.1
Consider this equation: \[\Large e^{\ln2} = 2 \] but: \[\Large e^{\ln2} = 2 ????? \] Rather view it like that: \[\Large e^{\ln2}=\left(e^{\ln2}\right)^{1}=\frac{1}{2} \]
 one year ago

SpacelimbusBest ResponseYou've already chosen the best response.1
and then you should get the same expression as I do.
 one year ago
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