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Snowcat [4.5K]
3 years ago
15

Find the equilibrium solutions of the ordinary differential equation

Mathematics
1 answer:
Mandarinka [93]3 years ago
3 0

Answer:

\dfrac{1}{2}\dfrac{sin y}{cos^2y}+\dfrac{1}{4}ln[\dfrac{siny +1}{siny-1}]=\dfrac{x^3}{3}+c  

Step-by-step explanation:

given,

y' =  x² (cos y)³

solve the equation using variable separable method

\frac{\mathrm{d} y}{\mathrm{d} x} = x^2 cos^3y\\\dfrac{dy}{(cosy)^3}= x^2 dx\\\dfrac{cos\ y}{cos^4 y}\ dy = x^2 dx\\\int \dfrac{cos\ y}{(1-sin^2 y)^2}\ dy = \int x^2dx\\\int \dfrac{1}{(t^2-1)^2}\ dt = \dfrac{x^3}{3}+c

here sin y  = t     :  cos y = dt

\int(\dfrac{1}{2}{[\dfrac{1}{t-1}-\dfrac{1}{t+1}]}^2 = \dfrac{x^3}{3}+c\\\dfrac{1}{4}\int [\dfrac{1}{(t-1)^2}-\dfrac{1}{t-1}+\dfrac{1}{t-1}+\dfrac{1}{(t+1)^2}]= \dfrac{x^3}{3}+c  

\dfrac{1}{2}\dfrac{sin y}{cos^2y}+\dfrac{1}{4}ln[\dfrac{siny +1}{siny-1}]=\dfrac{x^3}{3}+c  

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Suppose that a worker in Caninia can produce either 2 blankets or 8 meals per day, and a worker in Felinia can produce either 5
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Answer:

The answer to the question is

The war has caused the combined daily output of the two countries to decline by 50%

Step-by-step explanation:

To solve this we have

a worker at Caninia  produce Blankets = 2 and Meals = 8

a worker at Felinia produce Blankets = 5 and Meals = 1

Each country has 10 workers, therefore, total production rate for each of the two countries is

Caninia  produce Blankets = 20 and Meals = 80

Felinia produce Blankets = 50 and Meals = 10

Total production = Blankets = 70 and Meals = 90

Without trade between the two countries we have

Caninia  produce Blankets = 10 and Meals = 40

Felinia produce Blankets = 25 and Meals = 5

Total production = Blankets = 35 and Meals = 45

Therefore the war has caused the combined daily output of the two countries to decrease by

Initial  total production = Blankets = 70 and Meals = 90

Present total production = Blankets = 35 and Meals = 45

Difference in production= Blankets = 35 and Meals = 45

(Decline in production)/(Initial production)×100

For blankets → (35/70)×100 = 50 % decrease

For Meals → (45/90)×100 = 50 % decrease

Total decrease in daily output for the two countries = 50 %

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3 years ago
The sum of a number and two times a smaller number is 98. The bigger number is 22 less than three times the smaller number.
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<span>3a-22+2a=98 </span>

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<span>So the smaller number is 24 and the larger number is 50.</span>
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