f(x) = | = [" Vī+#dt.

Q: Use a computer algebra system to graph the slope field for the differential equation and graph the…

A: Given Data The integral is ꭍ03 xex²dx.   Let,

Q: Prove the formula.

A: Given a function Arc Sine Hyperbolic (t). We need to find the derivative of the function. Let's…

Q: Can i get help step by step please

A:

Q: Latel I, Vx2 + y² dV,

A: answer is in next step

Q: 1-dt 3- Ln(t) dt. Q10:- Calculate dx J2x t2

A: Use fundamental  theorem of calculus

Q: y' – y = 2te',

A: Laplace transform: L(y'(t))=py(p)-y(0) L(y(t))=y(p) L(2tet)=2(p-1)2

Q: find dx/dt at x = 3 if y = -5x^2-4 and dy/dt = -3. dx/dt =

A:

Q: Construct a linear first-order differential equation for which all solutions are asymptotic to the…

A:

Q: Find the general solution of the differential equation with the help of lablace transform

A:

Q: Find the derivative of the function. rcos(x) y = In(1+2t)dt sin(x)

A: Applying Leibniz rule

Q: 3. Water is being poured into a 10 liter leaky container so that the volume of the water, V,…

A: A differential equation is an equation that contains functions and their derivatives.  A…

Q: 15 dy dt 2-

A:

Q: find dx/dt at x=1 if y=3x^2+3 and dy/dt=1

A:

Q: The integrating factor of the differential equation xdy+ ydx= x3y6dy is

A:

Q: The differential equation of the family of curves orthogonal to x² + y? = C² is

A: Solve the above questions.

Q: 5. x- + Px = sin t %3D dt

A:

Q: What is the integrating factor of xy' + 6y = 3xy3?

A:

Q: Solve the differential cquation d'y by using the method of variation of parameters.

A:

Q: What is an integrating factor of the nonexact DE  (2y^2 + 3x) dx + xydy = 0 ?

A:

Q: solve the differential eq + 2x) dx = = (2y \1+x²y² |dy 1+x²y²

A: The given differential equation is: y1+x2y2+2xdx=2y-x1+x2y2dy

Q: Exercise 10. Find the derivative d 7x (* + 2) dt dx

A:

Q: What is the integrating factor of (y – cos² x) dx + cos xdy = 0?

A:

Q: Determine the integrating factor xydy - (y2-3x2)dx = 0

A:

Q: Find the general solution of the differential equation and check the result by differentiation.…

A: Given the differential equation:

Q: 2. Find the derivative of: (a) A(x) = [ 1n | In(sin(3t)) dt (b) A(x) = L, In(sin(3t)) dt

A: According to the Leibinitz rule :

Q: (§5.5, Q34) Calculate the derivative d dæ ), Vi dt.

A:

Q: у %3D V1+ 2х (1 — х)-3

A:

Q: 3. Calculate the derivative of f(x) = tan(4t) dt. %3D -1/16

A:

Q: 1. Solve the first derivative of f(x) = e-2x In x at x = 0.5 using forward finite-divided difference…

A: To find the first derivative of the function f(x) = e-2xlnx at x = 0.5 using forward finite-divided…

Q: 4. F(x) = (1-t) dt

A: To find the first derivative

Q: Calculate differential: f(x) = e-* cos(3x) + 2 of the range [1,2] with h=0.05 Using the backward…

A: Equation is  f(x)=e-xcos(3x)+2.Numerical differentiation method to find the solution.The value of…

Q: Find dx dt dx dt at x 2 if y= = - 2x² - 1 and dy dt = - 3.

A:

Q: ion dy 3t2 dt 2y + 2t3y' tion: ||

A:

Q: Find dx (e3t + 1)dt. -cos(3rx)

A:

Q: A population x of rats satisfies the DE dx /dt ka?. Initially there are x(0) = 2 rats, and their…

A: The general solution of a differential equation always contains a constant of integration. The…

Q: 4te dt TOT

A:

Q: Find dx dt dx dt at x = = 2 if y= 2x² - 1 and dy dt - 3.

A:

Q: Find the function ?(?) that satisfies the differential equation dy/dt - 2ty = -6t2et^2 and the…

A:

Q: . Use separable equations to find the general and particular solution of xy dx – (x +

A:

Q: 2 e -8; x(0) = 1 dt

A: Solution is given below:

Q: Find the derivative of the function. y = (3t – 1)(6t – 6) -1 dy dt II

A:

Q: d rIn(x) t tan(t) dt|. dx -1

A: we have to evaluate the following

Q: find the values of the derivatives ds/dt at t=-1 if s = 1 - 3t2

A:

Q: find the general solution of the differentialequation and check the result by differentiation.dy/ dt…

A: The given differential equation: dydt=x32 Integrate both sides of the differential equation with…

Q: 1. F(x) = S, t³ - 5t dt

A:

Q: What is the integrating factor of y' - 2xy x?

A:

Q: Find at x = -2 if y = - 4x² + 3 and dy dt dy dt = dx dt - 1.

A: Topic = Derivative As per guidelines , at a time only one question can be answered. pleas repost for…

Q: If you have the equation dx/dt = a,are you allowed to multiply both sides by dt to change the…

A: We have given,

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.