All categories

2 years ago

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

Mathematics

1 answer:

dmitriy555 [2]2 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

You might be interested in

An amount of $4000 was deposted in a bank of 7% compounded quarterly for 2 years. The rate the increased to 10% and was compound

GarryVolchara [31]

Answer:

$5599.20

Step-by-step explanation:

The quarterly interest rate for the first two years was ...

7%/4 = 0.0175

So, the multiplier each quarter for those 8 quarters was 1+0.0175 = 1.0175. At the end of the first 8 quarters, the account value had been multiplied by ...

1.0175^8

For the next 8 quarters, the quarterly interest rate was 10%/4 = 0.025. So at the end of those 8 quarters, the balance had been multiplied by ...

1.025^8

Then the balance at the end of 4 years was ...

$4000(1.0175^8)(1.025^8) ≈ $5599.20

The balance was $5599.20.

6 0

2 years ago

I needed some - with some bop in it-

Naya [18.7K]

I flew past the whip with that blunt in my mouth
Watch the swervin', that whip had a cop in it (Woo)

3 0

2 years ago

B. has 15 marbles and he got 123 more marbles add those two numbers and see what the number rounds to.

olganol [36]

Answer:

100 if rounded to hundreds

140 if rounded to tens

Step-by-step explanation:

7 0

3 years ago

Simplify the complex fraction: ((3x-7)/x^2)/(x^2/2)+(2/x)

Archy [21]

Simplify the complex fraction: ((3x-7)/x^2)/(x^2/2)+(2/x)

$\dfrac{ \dfrac{3x-7}{x^2} }{ \dfrac{x^2}{2} } + \dfrac{2}{x} =\qquad \qquad x \neq 0\qquad x^4 \neq 0 \\ \\ \\ \dfrac{(3x-7)*2}{x^2*x^2}+ \dfrac{2}{x} = \\ \\ \\ \dfrac{6x-14}{x^4}+ \dfrac{2}{x} =\\ \\ \\ \dfrac{ 6x-14 }{ x^4 }+ \dfrac{2(x^3)}{x(x^3)}=\\ \\ \\ \boxed{ \dfrac{ 6x-14 +2x^3}{ x^4 } }$

6 0

3 years ago

Hi!! Please help, thank you lots !!!

11Alexandr11 [23.1K]

3k²+11k+6, or (k+3)(3k+2), which is the 3rd one. :)

7 0

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