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3 years ago

Find the general solution of (2x² + y)dx + (x²y - x)dy = 0

Mathematics

1 answer:

dmitriy555 [2]3 years ago

8 0

Multiply the original DE by xy:

xy2(1+x2y4+1−−−−−−−√)dx+2x2ydy=0(1)

Let v=xy2, so that dv=y2dx+2xydy. Then (1) becomes

x(y2dx+2xydy)+xy2x2y4+1−−−−−−−√dxxdv+vv2+1−−−−−√dx=0=0

This final equation is easily recognized as separable:

dxxln|x|+CKxvKx2y2−1K2x4y4−2Kx2y2y2=−dvvv2+1−−−−−√=ln∣∣∣v2+1−−−−−√+1v∣∣∣=v2+1−−−−−√+1=x2y4+1−−−−−−−√=x2y4=2KK2x2−1integrate both sides

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Brilliant_brown [7]

Answer:

$the \: answer \: is \: c \: = - \frac{ \sqrt{14} }{5}$

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${ \sin }^{2}0 + \frac{11}{25} = 1 \\ { \sin }^{2}0 = \frac{14}{25}$

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2 years ago

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3 years ago

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If 32x+1 = 3x+5, what is the value of x? 2 3 4 6

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Answer:4

Step-by-step explanation:

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3 years ago

Find the distance between -6 - 8

Viefleur [7K]

Answer:

Number line.

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the diameter of the circle base of a storage container 18.8 m circumference of the base is approximately 59 m which of these cou

ozzi

Answer:

Estimate the value of pi =3.14

Step-by-step explanation:

The diameter of the circle base of a storage container 18.8m

The diameter of the circle 'd' = 2r

Given data 'd' = 2r = 18.8m

The circumference of the circle = 2πr

Given data of circumference of the circle = 59 m

given 2πr = 59

2r(π) = 59

18.8 π = 59 ( by using 2r =18.8)

π = 59/18.8

π = 3.13829

π = 3.14

Conclusion:-

Estimate the value of pi =3.14

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3 years ago

Find the general solution of (2x² + y)dx + (x²y - x)dy = 0​

Find the general solution of (2x² + y)dx + (x²y - x)dy = 0