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3 years ago

Find the general solution of the equation: x dy/dx + y = xe^x

Mathematics

1 answer:

ioda3 years ago

4 0

Step-by-step explanation:

x*(dy/dx) +y = x*(dy/dx) +1*y=x*(dx/dy)+dx/dx*y = (d(xy) /dx)

d(xy) /dx = x^ex<->

d(xy) =xe^x*dx

We integrate both parts with their respective variables.

Integral of d(xy) is xy+c.

Integral of xe^x*dx is equal to xe^x - e^x+c.

We have to integrate by parts:

Integral(x*e^x) = x*e^x - integral((x) 'e^x) = x*e^x - integral(e^x)= x*e^x-e^x.

We have that xy + c = x*e^x - e^x + c1, where c and c1 are non defined real constants.

So we get that xy= x*e^x - e^x + c2, where c2 is a real constant.

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What is -5.8+ (2.5) Evaluate expression

sweet [91]

-5.8 + (-2.5)

is just 5.8 - 2.5

Which is -8.3

8 0

3 years ago

Can someone plz help

GenaCL600 [577]

Step-by-step explanation:

$A=2πrh+2π {r}^{2}$

$= 2\pi.r(r + h)$

= 2π(14).(14+29)

=2π .14.43

$2 \times \frac{22}{7} \times 14 \times 43$

$= 2 \times 22 \times 2 \times 43$

=3784 mm²

8 0

3 years ago

Jeremiah currently has an account balance of $1624.35. His initial deposit on the account was $975 and it earned 3.7% simple int

Naya [18.7K]

Current Account Balance = $1,624.35

Initial Deposit = $975

Interest Rate (Simple) = 3.7% simple interest

Interest Earned = Current Account Balance - Initial Deposit

⇒ Interest Earned = $1,624.35 - $975

⇒ Interest Earned = $649.35

Now the Formula for Simple Interest is:

Simple Interest = × $\frac{\text{P x R x T}}{100}$ , where P is the initial deposit, R is the rate of interest and T is the time period

⇒ 649.35 = $\frac{\text{975 x 3.7 x T}}{100}$

⇒ T = $\frac{\text{649.35 x 100}}{\text{975 x 3.7}}$

⇒ T = 18

Hence, Jeremiah has had the account for 18 years.

6 0

3 years ago

Select all the rational numbers.

frez [133]

Answer:

1, 4, & 6

Step-by-step explanation:

1. is a fraction and fractions are rational numbers

2. 11 is not a perfect square so the answer should be a terminating decimal and terminating decimals are irrational numbers

3. is a terminating decimal and an irrational number

4. .23 is a decimal which is a rational number since it can be made into the fraction 23/100

5. is a terminating decimal which is an irrational number

6. is a fraction which is a rational number

Hope this helped and pls mark Brainliest

7 0

2 years ago

Read 2 more answers

Find the exact value by using a half-angle identity.cos five pi divided by twelve one divided by two times the square root of th

love history [14]

Answer:

+√[(2 - √3)/4]

Step-by-step explanation:

Here is the complete question

How do you find the exact values of cos(5pi/12) using the half angle formula?

Solution

The half-angle formula is

cos(θ/2) = ±√[(1 + cosθ)/2]

if cos(5π/12) = cos(θ/2) ⇒ θ/2 = 5π/12 ⇒ θ = 5π/6

So, θ = 5π/6 × 180/π = 150°

Cos150 = cos(180 - 30) = -cos30 = -cosπ/6 = -√3/2

So, cos(5π/12) = ±√[(1 + cos5π/6)/2]

= ±√[(1 + (-cosπ/6))/2]

= ±√[(1 - cosπ/6)/2]

= ±√[(1 - √3/2)/2]

= ±√[(2 - √3)/2 ÷ 2]

= ±√[(2 - √3)/4]

Since 5π/12 = 5π/12 × 180/π = 75° which is in the first quadrant, so

cos(5π/12) = +√[(2 - √3)/4]. We ignore the negative answer

6 0

3 years ago