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Sloan [31]
3 years ago
9

3. (6 Points). Solve the initial value problem y'-y.cosx=0, y(pi/2)=2e

Mathematics
1 answer:
Stells [14]3 years ago
7 0

Answer:

y=2e^{sin(x)}

Step-by-step explanation:

Given equation can be  re written as

\frac{\mathrm{d} y}{\mathrm{d} x}-ycos(x)=0\\\frac{\mathrm{d} y}{\mathrm{d} x}=ycos(x)\\\\=> \frac{dy}{y}=cox(x)dx\\\\Integrating  \\ \int \frac{dy}{y}=\int cos(x)dx \\\\ln(y)=sin(x)+c............(i)

Now it is given that y(π/2) = 2e

Applying value in (i) we get

ln(2e) = sin(π/2) + c

=> ln(2) + ln(e) = 1+c

=> ln(2) + 1 = 1 + c

=> c = ln(2)

Thus equation (i) becomes

ln(y) = sin(x) + ln(2)

ln(y) - ln(2) = sin(x)

ln(y/2) = sin(x)

y= 2e^{sinx}

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7 0
2 years ago
In Mr. Scott’s class the ratio of boys to girls is 2:3. The total number of students in Mr. Scott’s class is 30. What percent of
Yuri [45]

Answer:

40% of the class is Girls, so 12 students are girls

Step-by-step explanation:

add up the ratio

2+3=5

divide by 5

30/5=6

multipy ratio to find totial number of students

2*6=12

2*3=18

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5 0
3 years ago
How can I get to 75 using 7 5 6 3
eduard
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4 0
2 years ago
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Convert 120 degrees to radians in terms of pi.
shusha [124]
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8 0
3 years ago
Find the area of the figure.
Studentka2010 [4]

Answer:

SOLVE FOR RECTANGLE

Area: lw (length times width)

rectangle: lw (6x6)

AREA=36in

SOLVE FOR TRIANGLE B

Area: A=hbxb/2

A=hb/b2=6·6/2=18

TRIANGLE B=18in

SOLVE FOR TRIANGLE A

Area: A=hbxb/2

The height looks half the height as the other triangle

A=hb/b2=3·4/2=6

TRIANGLE A=6in

{ADD}

36+18+6

TOTAL: 60in

Step-by-step explanation:

HOPE THAT HELPED!!!

3 0
2 years ago
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