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Alex
3 years ago
11

Find general solution for y'' +y'-6y=12(e^3t+e^-2t)

Mathematics
2 answers:
garik1379 [7]3 years ago
6 0
 Homogeneous solution: <span><span>y′′</span>+<span>y′</span>−6y=0</span> yields the characteristic equation <span><span>r2</span>+r−6=0  ⇒  r=−3,2</span> So homogeneous part is <span><span>yc</span>=<span>C1</span><span>e<span>−3t</span></span>+<span>C2</span><span>e<span>2t</span></span></span>. Non-homogeneous solution: <span><span>y′′</span>+<span>y′</span>−6y=12<span>e<span>3t</span></span>+12<span>e<span>−2t</span></span></span> Use the method of undetermined coefficients. Suppose <span><span>yp</span>=A<span>e<span>3t</span></span>+B<span>e<span>−2t</span></span></span> is a solution, so you have <span><span><span><span>  yp</span>=A<span>e<span>3t</span></span>+B<span>e<span>−2t</span></span></span><span><span>y′p</span>=3A<span>e<span>3t</span></span>−2B<span>e<span>−2t</span></span></span><span><span>y′p</span>=9A<span>e<span>3t</span></span>+4B<span>e<span>−2t</span></span></span></span></span> Substitute into the original equation: <span><span><span><span>(<span>9A<span>e<span>3t</span></span>+4B<span>e<span>−2t</span></span></span>)</span>+<span>(<span>3A<span>e<span>3t</span></span>−2B<span>e<span>−2t</span></span></span>)</span>−6<span>(<span>A<span>e<span>3t</span></span>+B<span>e<span>−2t</span></span></span>)</span></span><span>6A<span>e<span>3t</span></span>−4B<span>e<span>−2t</span></span></span></span><span><span>=12<span>e<span>3t</span></span>+12<span>e<span>−2t</span></span></span><span>=12<span>e<span>3t</span></span>+12<span>e<span>−2t</span></span></span></span></span> This tells you that <span>A=2</span> and <span>B=−3</span>, and so your non-homogeneous part is <span><span>yp</span>=2<span>e<span>3t</span></span>−3<span>e<span>−2t</span></span></span>. Your final solution would be the sum of the non/homogeneous parts, or <span>y=<span>yc</span>+<span>y<span>p</span></span></span>
castortr0y [4]3 years ago
3 0
Am i correct? Your solution would be <span><span>y=<span>yc</span>+<span>yp</span></span></span>
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an octupos weights 5/6 kiligrams after two weeks it weights 3/5 kilograms afterwards it lost 1/5 kilograms how much does d=the o
arsen [322]

Answer:

5/6+3/5+1/5=d

Step-by-step explanation:

4 0
2 years ago
p borrowed Rs. 16000 from a person at 12 % per Annum simple interest and lent the whole amount to Q at the same rate of annually
hichkok12 [17]

Answer:

P earned $ 718.85.

Step-by-step explanation:

Given that P borrowed $ 16000 from a person at 12% per annum simple interest and lent the whole amount to Q at the same rate of annually compound interest, to determine how much did he gain after 3 years the following calculation must be performed:

16,000 x 0.12 x 3 = X

1,920 x 3 = X

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16,000 x (1 + 0.12 / 1) ^ 3 = X

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22,478.85 - 16,000 = 6,478.85

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5 0
3 years ago
X - 0.1x = 54 <br> Is x = 60 a solution
sashaice [31]

Answer:

yes

Step-by-step explanation:

60 - 0.1(60) = 54

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54 = 54

8 0
3 years ago
Read 2 more answers
Will mark Brainliest!! :)
Georgia [21]

Step-by-step explanation:

The system of equations for eq 1 which is 3x + y = 118 represents the Green High School which filled three buses(with a specific number of students identified as x) and a van(with a specific number of students identified as y) with a total of 118 students.

for eq 2; 4x + 2y = 164; represents Belle High School which filled four buses(with a specific number of students identified as x) and two vans(with a specific number of students identified as y) with a total of 164 students.

The solution represents the specific number of students in the buses and vans in eq1 and eq 2 with x being 36 students and y being 10 students.

substituting 36 for x and 10 for y in eq 1;

3(36) + 10 = 108 + 10 = 118 total students for Green High School

substituting 36 for x and 10 for y in eq2;

4(36) + 2(10) = 144 + 20 = 164 total students for Belle High school

6 0
2 years ago
A car drives at a rate of 65 mi/hr. what is the speed of the car in ft/s? note: 1 mi = 5280 ft
lana66690 [7]

Answer:. 95.33 ft/sec

Multiply 65 by 5280 to get 343200 feet per hour. Then Divide by 3600. There are 60 minutes in an hour, and 60 seconds in a minute.

343200 ÷ 3600 = 95.333

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
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