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cluponka [151]
3 years ago
9

First-order linear differential equations

Mathematics
1 answer:
garik1379 [7]3 years ago
4 0

Answer:

(a) \frac{dy}{(2y+1)}=tdt (b) y=\frac{e^{t^2}+e^{2c}-1}{2}

Step-by-step explanation:

(1) We have given \frac{dy}{dt}+ycost=0

\frac{dy}{dt}=-ycost

\frac{dy}{y}=-costdt

Integrating both side

lny=-sint+c

y=e^{-sint}+e^{-c}

(2) \frac{dy}{dt}-2ty=t

\frac{dy}{dt}=2ty+t

\frac{dy}{dt}=t(2y+1)

\frac{dy}{(2y+1)}=tdt

On integrating both side  

\frac{ln(2y+1)}{2}=\frac{t^2}{2}+c

ln(2y+1)={t^2}+2c

2y+1=e^{t^2}+e^{2c}

y=\frac{e^{t^2}+e^{2c}-1}{2}

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Solve the equation
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Answer:

x ≈ - 5.32, x ≈ 1.32

Step-by-step explanation:

Given

x² + 4x - 7 = 0 ( add 7 to both sides )

x² + 4x = 7

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(2)x + 4 = 7 + 4

(x + 2)² = 11 ( take the square root of both sides )

x + 2 = ± \sqrt{11} ( subtract 2 from both sides )

x = - 2 ± \sqrt{11}

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x = - 2 - \sqrt{11} ≈ - 5.32 ( to 2 dec. places )

x = - 2 + \sqrt{11} ≈ 1.32 ( to 2 dec. places )

4 0
3 years ago
After driving to a riverfront parking lot, Bob plans to run south along the river, turn around, and return to the parking lot, r
mars1129 [50]

Answer:A) 1.5

Step-by-step explanation: Bob runs at the rate of 8mins per mile

In 60mins his rate would be=60/8=7.5

Let a be the distance he further runs south

2s+3.25

Total distance covered in 50mins=Time=distance/speed=

50/60

50/60=2s +3.25/7.5

Cross multiply

60(2s+3.25)=50×7.5

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I don’t understand what the answer is
lina2011 [118]

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Step-by-step explanation:

7 0
3 years ago
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What is 3÷1/4 please tell me
Lady bird [3.3K]
The answer to your question
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7 0
3 years ago
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Suppose that LMN is isosceles with base LN suppose that M
ira [324]

Given:

In an isosceles triangle LMN, LM=MN.

m\angle M=(3x+17)^\circ,m\angle L=(2x+36)^\circ

To find:

The measure of the angles L, M and N.

Solution:

In triangle LMN,

LM=MN                     (Given)

m\angle N=m\angle L=(2x+36)^\circ   (Base angles of an isosceles triangle are equal)

Now,

m\angle L+m\angle M+m\angle N=180^\circ

(2x+36)^\circ+(3x+17)^\circ+(2x+36)^\circ=180^\circ

(7x+89)^\circ=180^\circ

(7x+89)=180

On further simplification, we get

7x=180-89

7x=91

x=\dfrac{91}{7}

x=13

The value of x is 13. Using this value, we get

m\angle L=(2(13)+36)^\circ

m\angle L=(26+36)^\circ

m\angle L=62^\circ

Similarly,

m\angle M=(3(13)+17)^\circ

m\angle M=(39+17)^\circ

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And,

m\angle N=m\angle L

m\angle N=62^\circ

Therefore, the measure of angles are m\angle L=62^\circ,m\angle M=56^\circ,m\angle N=62^\circ.

5 0
3 years ago
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