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 Ly(x)] = 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)]. 81(7 – s²) s(s? + 81) Y(s)

Q: a particle moves along a curve y = (2x² + 5x)°, calculatey (0) and what is the interpretation of the…

A: Let us considre the function y=f(x) The derivative the function is denoted as dydx=f'(x) Derivative…

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: Suppose the slope of the tangent lir

A: Given that the slope of the tangent line at any point on a curve is…

Q: consider y'=-2y,y(0)=1 and analytic solution is y(x)=e^-2x a.Approximate y(0.1) using two steps of…

A:

Q: 1. Solve the following DE's (for y as a function of x, where possible): a) xy'= y – 2y, with y(1) =…

A:

Q: find Using your results from problem #3 the equation of the tangent line for f(x)... when -20 2-2…

A: We have to find the tangent line equation

Q: 5. In rectangular coordinates verify that V · V x A = 0 where A = xyz(ê+ ŷ + 2) by carrying out the…

A:

Q: Find y' if y = x* Inx

A: Differentiate the given function using the product rule. y'=ln xddxx4+x4ddxlnx Use the standard…

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: 5. Find the equation of the tangent line for: x = vt + 9, y= at (4,-)

A: The objective is to find the equation of the tangent line.

Q: The integrating factor (IF) of the equation y' - 2ycot2x O A. sin2x O B. cot2x O C. Lnsin2x…

A: Solution:  To find the integrating factor of the given differential equations

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

A:

Q: tS W C (b) Suppose that a function h is such that h(-1) 5 and h'(x) 2x +3. Find the equation of the…

A: The derivative of the function h(x) is given by,

Q: Find y' for (ry)”/” – 64 at the point (4,4). (wy)³/2 C At (4, 4), g' DE

A:

Q: Find y' if y = In(9x² + 5y²). y' = X

A: The given data is: y=ln(9x2+5y2)  Find y'

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: 19. The slope of the tangent to the curve (x2 + y²)² = 4.x²y at the point (1, 1) is 3 3 (a) - () – 1…

A: We have to find slope of the tangent to the curve x2+y22=4x2y at the point 1, 1. We know slope of…

Q: Given (x³ + y² + 7)* = 4x + 3y + 9, (a) find y', (b) find the equation of the tangent line at…

A:

Q: Sketch the graph of y'=ly with y(0) = 1 yo

A: Given :

Q: Let h(y) = (2y – 3)4 Determine the derivative of h. h'(y) 8 (2y-3) 5 ✓ h is differentiable on 05…

A:

Q: 7. Find y'if y=x³+ sin (x)

A: given

Q: B. find y' and y" 5x+2 1. y = %3D 3x-7 2. y = (x2 +x + 1)2 C. 1. If f(x) = Vx find,f '(4) and f "(4)

A: Topic = Derivative As per guidelines , At a time only three sub-parts can be answered. please repost…

Q: of y = 2 tan x 1-tan²x

A: Solution is done in step 2

Q: (4) Find y' if y = xcot-12x -V1– 4x².

A:

Q: y = cos(r) fonksiyonunun birinci mertebeden türevini z = noktasında h = olmakla 3-nokta aranokta…

A: Given function is fx=cosx. We have to evaluate the first derivative of fx=cosx at x=π2 and h=π4. The…

Q: If function a solution of differiential equation? Shoe work  y=sqrtx; xy'-y=0 y=x^3; x^2y" -6y=0

A:

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

A:

Q: Show that the curve y = 6x + 6x - 3 has no tangent line with slope 2.

A:

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.