Question

The differential equation dy/dx = y/x^2 has a solution given by:

Answer 1

y= C sqrt(x^2+4)
y= Ce^(-1/x)
y=1/2e^(x^2) + C
x^2+y^2=C
y= Ce^(-kt)

Answer 2

Hi!

Answer 3

Hi

Answer 4

1. Compute the integral Int(x*exp(-x^2),x=0..1)

a) 1/e b) 1/2 c) (1/2)(1-1/e) d) (1/e-1) e) -1/(2e)

SOLUTION: The answer is C. The antiderivative is

2
- 1/2 exp(-x )

Inserting the limits 0 and 1, we obtain -(1-1/e)/2. which is response C.



2. There is a chemical reaction involving the compound N_2 O_5.
Let C(t) denote the concentration of N_2 O_5 as a
function of time t measured in seconds. This
concentration satisfies

dC/dt = -0.05C(t)

How long (in seconds) will the reaction take to reduce the
concentration to 10% of its original value?

a) 10/(e^(-.05)) b) (e^(.05))/10 c) .05/ln(10) d) .05 ln(1/10) e) ln(10)/(.05)

SOLUTION: The answer is E. The solution to the given differential equation
is C(t)=K e^(-.05t), where K is the inititial concentration. We seek the time t
when C(t)=K/10 (one tenth the initital concentration). Setting K/10=K e^(-.05t)
and solving for t (by taking natural logs) gives t=ln(1/10)/(-.05).
Since ln(1/10)= -ln(10), this becomes t=ln(10)/(.05), which is response E.

Answer 5

u can see in this example equation the form used

Answer 6

This equation is separable. Get y and dy on the same side and x and dx on the other.

Answer 7

this is how we will solve ours

Answer 8

excuse me @peachpi do not interrupt please, it is rude.

Answer 9

@pandaluvs I'm confused. What am I supposed to do?

Answer 10

the answer is E

Answer 11

How do you know that?

Answer 12

done the equation before

Answer 13

:D :)

Answer 14

Alright thanks

Answer 15

no prob.

Answer 16

um, no. FYI
\[\frac{ dy }{ dx }=\frac{ y }{ x^2 }\]
Cross multiply to separate the variables
\[\frac{ dy }{ y }=\frac{ dx}{ x^2 }\]
Integrate both sides. Put the constant of integration on the right
\[\int\limits\frac{ dy }{ y }=\int\limits\frac{ dx}{ x^2 }\]
\[\ln y = {-\frac{ 1 }{ x }+C}\]
Make both sides the exponent of e
\[y=e ^{-\frac{ 1 }{ x }+C}\]
Break apart the exponent
\[y=e ^{-\frac{ 1 }{ x }}*e^C\]
Rewrite e^C as one constant
\[y=Ce ^{-\frac{ 1 }{ x }}\]

Answer 17

That's the answer I got as well after looking over it again. I was not so sure about panda's answer....

Answer 18

Thanks @peachpi