t² - t dt 0, = (x)6 g'(4) =

Q: Use an Integrating Factor to solve the differential equation.

A:

Q: Find the differential d4y of the function y=x5.

A:

Q: Find the second derivatives. d2/dt2 (t2 ln t)

A: Given: d2dt2(t2log t)

Q: Is y'' = sin x a linear differential equation?

A:

Q: Classify the differential equation as separable or linear (1+2*); dy = 4y dx

A: To classify the differential equation as linear or separable.

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

A: Given differential equation is

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

A: Use fundamental  theorem of calculus

Q: Solve the differential equation by variation of parameters. y" + 2y + y = et In(t) y(t)

A:

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: Solve the differential equation by variation of parameters. y" + 2y' + y = et In(t) y(t) =

A:

Q: Find the differential of the function y=√x3+4x at x=2.

A: Given the function:

Q: Calculate the differential of the function y=x5−7x3+5x at the point x=2 when dx=0,2.

A:

Q: Solve the differential equation using separation of variables: dy + y² +y= 0 dx

A: The given DE is: xdydx+y2+y=0...(1)

Q: Use integration to find a general solution of the differential equation       dy/dx = e2−x

A: dydx= e2-xdydx= e2e-xdy = e2e-xdxThis is variable separable form

Q: Use integration to find a general solution of the differential equation                  dy/dx =…

A:

Q: e*dx cln 1 Calculate Jin 0.5 V1-ezx" (b)

A: We will solve this integral via substitution:

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: Verify that y(x)=exsinx is a solution to the differential equation   2ycotx-d2y/dx2=0

A: Consider the given solution to the D.E. Differentiate it w.r.t x twice to get the double derivative…

Q: Calculate the differential of the function y=2x x2−3 at the point x=3 when dx=−315.

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: What is the linear differential equation of dy/dx+2xy+xy^4=0 using dv/dx?

A:

Q: Find the differential equation of dy/dx = x+y/x-y

A:

Q: dy + y² +y =0 dx

A:

Q: Find the differential d3y of the function y=xsinhx.

A:

Q: dy (sec x) dx eуtsin x

A: Given : The differential equation sec xdydx = ey + sin x

Q: Solve the differential equation by variation of parameters. y" + 2y' + y = e-t In(t) y(t) =

A:

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

A: Given the differential equation:

Q: he integrating factor to the linear differential equation x(x² +1)y' +2y = (x² +1)° is:

A:

Q: Find the differential of the function y=2x2+3x+1 at the point x=1 when dx=0,1.

A: To find the differential of the given function at point x = 1 when (d x) = 0, 1.

Q: Solve the differential equation using Variation of Parameters (D² – 2D + 1)y

A:

Q: 53. df = (x+ 1)ye"dx + xe*dy

A:

Q: Find the differential d3y of the function y=x2ex.

A:

Q: Use integration to find a general solution of the differential equation                  dy /dx = x…

A: Given: dydx=x1+x2 Multiply both sides by dx dy=x1+x2dx

Q: dy = ky| 1- dx L)

A:

Q: Find the differential d3y of the function y=1/√x.

A:

Q: Solve the differential equation using separation of variables: dy + y* + y = 0 dx

A:

Q: dy/dt = y(1-y) y1(0) = 9, y2(0) = -1 What do y1 and y2 mean? The first and second derivatives?

A:

Q: Find the differential dy of the given function. y = csc 3x Jax dy Need Help? Read It

A: dy = ? dx

Q: dy +2xy = e-* is The integrating factor of the differential equation

A: By using linear differential equations integrating factory  we can calculate..

Q: Find the differential of y=xsinπx2 at the point x=12 when dx=0,01.

A: We will use product rule and chain rule to find dy/dx

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

A:

Q: The population of fish in a lake grows logistically according to the differential equation where t…

A: Logistic growth model of fish is given by dydt=0.1y1-y2500                      (1) Initially lake…

Q: Xoly-yolx- Jrig? dXこ0

A: For checking the function is homogeneous or not , firstly we find dydx and then we calculate the…

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

A: we have to evaluate the following

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: Solve the differential equation using separation of variables: dy +y° +y=0 dx

A: The detailed solution is given below Thank you

Q: Solve the differential equation by variation of parameters. y" - 2y + y = et arctan(t) y(t):

A:

Q: Solve the differential equation by variation of parameters. y" + 2y + y = et In(t) y(t) =

A: Given : The given differential equation is y''+2y'+y=e-tln(t). To find: The solution y(t) for the…

Q: Calculate the increment and differential of the function y=x2−x+1 at the point x=2 when dx=1.

A: Given, the function is y = x2 -x +1 at the point x = 2 and dx = 1, We have to calculate the…