L[y(x}] = Y(s) olmak üzere, y(x) 'e göre bir başlangıç değer problemine Laplace dönüşümü uygulandığında aşağıda verilen denklem elde edilmiştir. Buna göre y(0) değerini bulunuz. [Let L[y(z)] = Y(s) the following equation has been obtained when Laplace transformation has been applied to an initial value problem in y(x). Find y(0)]. 16(4 – s2) s(s² + 16)' Y(s) = Lütfen birini seçin: O 18 O 16 O-18 O-17 O -16

Q: Find y' at the point (6, 6) where x sin(x? – y²) + 33 = x? – 3.

A:

Q: Find y' and y". y - In(x + VB+ x²) / 8 + x² 1 y' = V 8 +x2 y" II

A: Given: y=lnx+8+x2

Q: 2. a). Find the velocity and acceleration of a particle whose position function is x(t)=…

A:

Q: Find the length of the curve below from the the point P = (1, 2) to the point Q = (8, 5). 2² = (y –…

A: The length of arc for curve y=fx from x=a to x=b is given as follows. L=∫ab1+dydx2dx The given curve…

Q: Find y' and y". In(7x) y = x7 y' = y" %3D

A: The given function is: y=ln(7x)x7 Therefore, y'=1x7ddx(ln(7x))+ln(7x)ddx1x7    =1x717x·7+ln(7x)-7x8…

Q: Find y ' if xº = y* .

A: Given problem:- xy =yx  To find:- y'

Q: Find G′(w) if G(w)=5/ 9w^5 +7 sqaure root w. G'(w)

A:

Q: dy −2r — 9 (a) Show that = dx x + 2y (b) Find the two points where the curve given by the original…

A: Given- Consider the equation x2 + xy + y2 = 19.  To find-  Show that dydx = -2x - yx + 2y.  Find…

Q: Tangent to the curve z2 = 2xy + x2 , z = 3 , at the point ( 1, 4, 3) %3|

A: For a surface of the form: f(x, y, z)=0, the equation of the tangent at x0, y0, z0 is defined as…

Q: If t²y" – ty – y = 0 ,y(1) = 3 and y'(1) = -1, then y(4) = . . . %3D

A: Given differential equation, t2y''-12ty'-y=0,y1=3,y'1=-1 Find the value of y4.

Q: Find y' of cot (xy2) + xy = x².

A: Given query is to find derivative of the expression.

Q: ) y = -3 ln x + 3x

A:

Q: Differentiate. y = In (4x² - 7x+9) y'=0

A: The function is The aim is to find the derivative of the function

Q: Find y" * y" at (1,1) of x'y =1

A: We have to find derivative

Q: Find y' if x = y*. C Note: Leave your answer in terms of ï and y. y

A:

Q: ) Find the equation of the line normal to the curve x'y+ y'x = 10 at point (1,2).

A: Slope of a normal to the function y=f(x) at point m,n is given by the value of -dxdy at m,n Equation…

Q: Find y' if y= is-2x(+)* +

A:

Q: Find y as a function of a if y(1)9, y'(1) = -5. y = x²y" - 15xy' + 64y = x²,

A:

Q: Eliminate the arbitrary constants y Iny = C,e "+ C, X-

A:

Q: I SLOPE & TANGENT LINE OF x = +₁², ₁y₁ = +²³₁ -·3+ at (3,0).

A:

Q: Knowing that the plane tangent to the graph f(x,y) at the point (1,4,f(1,4)) is  x + 2y + 3z = 4…

A: Given  that the plane tangent to the graph f(x,y) at the point (1,4,f(1,4)) is  x + 2y + 3z = 4 and…

Q: Find the x and y coordinates on the graph of f (x) = x³ - 3x where the tangent is horizontal. (A)…

A:

Q: 4. xyzx + 2y³ (2)³ = 1 Dependent variable/s: Independent variable/s: Type: Order: Degree: Linearity:

A: Solution :  To discuss about the nature of given differential equations

Q: The slope of the curve y=x' +3x² – 6x +5 at (1,3) is -

A:

Q: Find y' and y'' given x2 +xy +y2 =1

A:

Q: Find y' and y". x³y³ = y – 4

A: Explanation of the answer is as follows

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.