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3 years ago

8

Math Help?? What is the value of X?

1 answer:

gregori [183]3 years ago

6 0

Heres an example i dont have the anwser to your question tho Hope i helped(1) x + 2y = 4

<span>(2) 5x + y + 15 = 3x - 3y + 23</span>

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Find a second solution y2(x) of<br> x^2y"-3xy'+5y=0; y1=x^2cos(lnx)

rosijanka [135]

We can try reduction order and look for a solution $y_2(x)=y_1(x)v(x)$ . Then

$y_2=y_1v\implies{y_2}'=y_1v'+{y_1}'v\implies{y_2}''=y_1v''+2{y_1}'v+{y_1}''v$

Substituting these into the ODE gives

$x^2(y_1v''+2{y_1}'v+{y_1}''v)-3x(y_1v'+{y_1}'v)+5y_1v=0$

$x^2y_1v''+(2x^2{y_1}'-3xy_1)v'+(x^2{y_1}''-3x{y_1}'+5y_1)v=0$

$x^4\cos(\ln x)v''+x^3(\cos(\ln x)-2\sin(\ln x))v'=0$

which leaves us with an ODE linear in $w(x)=v'(x)$ :

$x^4\cos(\ln x)w'+x^3(\cos(\ln x)-2\sin(\ln x))w=0$

This ODE is separable; divide both sides by the coefficient of $w'(x)$ and separate the variables to get

$w'+\dfrac{\cos(\ln x)-2\sin(\ln x)}{x\cos(\ln x)}w=0$

$\dfrac{w'}w=\dfrac{2\sin(\ln x)-\cos(\ln x)}{x\cos(\ln x)}$

$\dfrac{\mathrm dw}w=\dfrac{2\sin(\ln x)-\cos(\ln x)}{x\cos(\ln x)}\,\mathrm dx$

Integrate both sides; on the right, substitute $u=\ln x$ so that $\mathrm du=\dfrac{\mathrm dx}x$ .

$\ln|w|=\displaystyle\int\frac{2\sin u-\cos u}{\cos u}\,\mathrm du=\int(2\tan u-1)\,\mathrm du$

Now solve for $w(u)$ ,

$\ln|w|=-2\ln(\cos u)-u+C$

$w=e^{-2\ln(\cos u)-u+C}$

$w=Ce^{-u}\sec^2u$

then for $w(x)$ ,

$w=Ce^{-\ln x}\sec^2(-\ln x)$

$w=C\dfrac{\sec^2(\ln x)}x$

Solve for $v(x)$ by integrating both sides.

$v=\displaystyle C_1\int\frac{\sec^2(\ln x)}x\,\mathrm dx$

Substitute $u=\ln x$ again and solve for $v(u)$ :

$v=\displaystyle C_1\int\sec^2u\,\mathrm du$

$v=C_1\tan u+C_2$

then for $v(x)$ ,

$v=C_1\tan(\ln x)+C_2$

So the second solution would be

$y_2=x^2\cos(\ln x)(C_1\tan(\ln x)+C_2)$

$y_2=C_1x^2\sin(\ln x)+C_2x^2\cos(\ln x)$

$y_1(x)$ already accounts for the second term of the solution above, so we end up with

$\boxed{y_2=x^2\sin(\ln x)}$

as the second independent solution.

6 0

4 years ago

Simplify this expression<br> -2x + 3 -(5-6x)

Vlad1618 [11]

Answer:

75

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Evan uses some of his comic-book money to buy a magazine for $4. If Evan's uncle gave him $30, what fraction of this money did h

DochEvi [55]

Answer:

2/15 fraction of money is spend to buy magazine.

Step-by-step explanation:

Total Money given by Evan's uncle = $30

Money spent by Evan to buy magazine = $4

Fraction of money spend on magazine = Money spent by Evan to buy magazine ÷ Total Money given by Evan's uncle

⇒ 4/30 = 2/15

Hence 2/15 fraction of money is spend to buy magazine.

lets check our answer.

2/15 of Total Money given by Evan's uncle = (2/15 )× 30 = 2 × 2 = 4

so $4 represents 2/15 of $30 , hence our solution is correct .

6 0

3 years ago

Pleaseeee helppp due in 8 minutesss please!!

sertanlavr [38]

Answer:

B 5x=34.5

it's too easy in which class you studies

6 0

3 years ago

Read 2 more answers

b) 20 labourers complete the construction of a building in 24 days. In how many days would 16 labourers complete the constructio

defon

Answer:

16 labourers complete the construction

in 30 days

Step-by-step explanation:

mark me as a brainlist answer

3 0

3 years ago