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sergiy2304 [10]
3 years ago
8

Solve the differential equation 3ydx+(xy+5x)dy=0

Mathematics
2 answers:
drek231 [11]3 years ago
8 0

Answer:

-3㏑x+C=y+5㏑y

Step-by-step explanation:

Given differential equation is separable,

3ydx +(xy+5x)dy= 0

3ydx=-(xy+5x)dy

taking x as common,

3ydx=-(y+5)xdy

-3/xdx=(y+5)/ydy

-3/xdx=(1+5/y)dy

integrating both sides of equation,

∫-3/xdx=∫(1+5/y)dy

-3㏑x+C=y+5㏑y which is the solution of given ordinary differential equation.C is the constant of integration.


Brrunno [24]3 years ago
4 0

The ODE is separable:

3y\,\mathrm dx+(xy+5x)\,\mathrm dy=0\implies x(y+5)\,\mathrm dy=-3y\,\mathrm dx\implies\dfrac{y+5}y\mathrm dy=-\dfrac3x\,\mathrm dx

Integrating both sides gives

\displaystyle\int\left(1+\frac5y\right)\,\mathrm dy=-3\int\frac{\mathrm dx}x\implies y+5\ln|y|=-3\ln|x|+C

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Answer:

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Step-by-step explanation:

To know if x = 5 satisfy the equation or not, you just have to applied it into your equation:

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Hope this help you :3

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1 year ago
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gavmur [86]

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Which choice best reflects the overall sequence of
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The writer begins this passage by stating that the ability of birds to fly has long been a source of debate among scientists.

The article then goes on to explain that when a group of students challenged Ken Dial to come up with new data on this hotly debated topic, he devised an experiment to study the evolution of flight by observing how baby Chukars learn to fly. Dial noted the unusual way the little Chukar "used its wings and legs cooperatively" to climb over hay bales during the experiment. Following that, he devised a series of experiments to investigate his discovery.

<h3>Below is the passage mentioned in the question is from Thor Hanson, Feathers by Thor Hanson - </h3>

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.............................................................

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ground-up hypothesis). "

To learn more about passages from the given link

brainly.com/question/27860285

#SPJ4

7 0
1 year ago
How many 3 3/4 inch wires can be cut from a spool of wire that is 100 inches long. Will there be any wire left over? If so, how
lisabon 2012 [21]
You \ have\ to\ divide\ 100\ by\ 3\frac{3}{4}:\\\\100:3\frac{3}{4}=\\\\\frac{400}{4}:\frac{15}{4}=\\\\\frac{400}{4}\cdot\frac{4}{15}=\\\\\frac{400}{15}=\frac{80}{3}=26\frac{2}{3}\\\\Can\ be\ cut\ 26\ wires.
7 0
2 years ago
Read 2 more answers
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