HELP PLEASE!!!!!!!!!

Dy/dx = (sin x)/y , y(0) = 2

Scorpion4ik [409]

Answer:

The solution for this differential equation is $y=\sqrt{-2cos(x)+6}$

Step-by-step explanation:

This differential equation $\frac{dy}{dx}=\frac{sin(x)}{y}$ is a separable First-Order ordinary differential equation.

We know this because a first-order differential equation is separable if and only if it can be written as

$\frac{dy}{dx}=f(x)g(y)$ where <em>f</em> and <em>g</em> are known functions.

And we have

$\frac{dy}{dx}=\frac{sin(x)}{y}\\ \frac{dy}{dx}=sin(x)\frac{1}{y}$

To solve this differential equation we need to integrate both sides

$y\cdot dy=sin(x)\cdot dx\\ \int\limits {y\cdot dy}= \int\limits {sin(x)\cdot dx}$

$\int\limits {y\cdot dy}=\frac{y^{2} }{2} + C$

$\int\limits {sin(x) \cdot dx}=-cos(x) + C$

$\frac{y^{2} }{2} + C=-cos(x) + C$

We can make a new constant of integration $C_{1}$

$\frac{y^{2} }{2}=-cos(x) + C_{1}$

We need to isolate y

$\frac{y^{2} }{2}=-cos(x) + C_{1}\\y^2=-2cos(x)+2*C_{1}\\\mathrm{For\:}y^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}y=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\y=\sqrt{-2cos(x)+c_{1} } \\y=-\sqrt{-2cos(x)+c_{1} }$

We have the initial conditions y(0)=2 so we can find the value of the constant of integration for $y=\sqrt{-2cos(x)+c_{1} }$

$2=\sqrt{-2\cos \left(0\right)+c_1}\\2= \sqrt{-2+c_1} \\c_1=6$

For $y=-\sqrt{-2cos(x)+c_{1} }$ there is not solution for $c_{1}$ in the domain of real numbers.

The solution for this differential equation is $y=\sqrt{-2cos(x)+6}$

8 0

2 years ago

How do you solve a monomials when there is a number in front of the parentheses

iren [92.7K]

Answer:

you take the number outside of the parentheses and multiply it by everything inside of the parentheses.

Step-by-step explanation:

3 0

2 years ago

Si una bolsa de plástico pesa cuatro kilogramos y contiene tres latas con atún y dos de mermelada, y en otra bolsa contiene dos

Lerok [7]

Step-by-step explanation:

which language is this.?... try to upload in English..

you may get answers from so many people..

3 0

2 years ago

Which equation, when graphed, has x-intercepts at (8,0) and (-2,0) and a y-intercept at (0,-48)?

ludmilkaskok [199]

Answer:

3rd answer f(x) = 3(x-8)(x+2)

Step-by-step explanation:

The x-intercepts are the points at which the parabola intersects the x-axis.

Function y = a(x - r₁)(x - r₂) is in factored form, where r₁ and r₂ are x-intercepts so if r₁ = 8 and r₂ = -2 then

y = a (x-8)(x-(-2))=a(x-8)(x+2)

For y intercept plug in (0,-48) in equation and calculate a:

-48 = a (0-8)(0+2)

-48 = a(-8)(+2)

-48 = -16a divide by -16

a = 3

Function is y = 3(x-8)(x+2)

6 0

2 years ago

Please write your answer below !!!

Paladinen [302]

A.) We know, sum of the complimentary angles is equal to 90.
So, Equation: 15 + x = 90

B.) Solving: 15 + x = 90
x = 90 - 15
x = 75

In short, Your Answer would be 75

Hope this helps!

6 0

2 years ago