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ksaimouli
 2 years ago
find particular solution y=f(x
ksaimouli
 2 years ago
find particular solution y=f(x

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

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

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

Spacelimbus
 2 years ago
Best ResponseYou've already chosen the best response.1Integrate both sides.

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

ksaimouli
 2 years ago
Best ResponseYou've already chosen the best response.0they have given f(1)=2

Spacelimbus
 2 years ago
Best ResponseYou've already chosen the best response.1You 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.

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

Spacelimbus
 2 years ago
Best ResponseYou've already chosen the best response.1Almost, 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.

ksaimouli
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1360441531205:dw

ksaimouli
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1360441583641:dw

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

Spacelimbus
 2 years ago
Best ResponseYou've already chosen the best response.1and then you should get the same expression as I do.
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