Verify for a > 0, that y = is a solution of the nonlinear differential equation yyll = x.

Q: 2. Show that y = e-6t satisfies the differential equation y" – y – 42y = 0.

A: We have to verify that y''-y'-42y=0 when y=e-6t. We know that d2ydt2=y''dydt=y'de-atdt=-ae-at So…

Q: Let y' (x) = V1– y²(x) be a differential equation. What is a solution?

A:

Q: The equation y + xy2 =0, is a homogeneous non-linear differential equation True False

A: See solution below

Q: Find the general solution of the first order differential equation (x+2) y′ + 4y = (3x + 6)-2 lnx.

A: Given: x+2y'+4y=3x+6-2lnx for finding solution of given differential equation, first we convert it…

Q: 5. Use a substitution to solve the nonlinear differential equation: (y + 1)y" = (y )²

A: We have to evaluate: (y(x) + 1) ( d^2 y(x))/( dx^2) = (( dy(x))/( dx))^2:Treating y as the…

Q: Solve the Higher Order Linear Differential Equation: yiv – y’’’ + 2y’ = 0

A:

Q: Find general solution of the Euler differential equation x2y” + 3xy’ - 3y = 0

A: x2y” + 3xy’ - 3y = 0

Q: Find the general solution of the first-order linear differential equation y′ + 3y = e3x for x >…

A:

Q: Find the gene solution of the differential equation y+2xyy'-e-2yy'=0

A:

Q: find the general solution of the first-order linear differential equation. y' + y = ex

A:

Q: Obtain the solution of the differential equation y′ = (x + y)^2

A: Given differential equation is: dydx=(x+y)2                       (1) Let us assume (x+y)=t…

Q: ex 2. y" — 2у' + у %3 1+ x2

A:

Q: 1 Verify if y = -+; xy + y = x² is a solution of a differential equation.

A: We have to verify the solution

Q: Find the general solution of the first-order linear differential equation y′ − y = 10

A:

Q: The differential equation y' = e3x+Iny is linear and separable. %3D Select one: True False

A:

Q: Find the solution of the differential equation that satisfies the given initial condition. dy xp…

A: see 2nd step

Q: Write an equivalent first-order differential equationand initial condition for y

A: We have to write an equivalent first-order differential equation and initial condition for y…

Q: Find the solution of the Linear Homogenous Differential Equation with Constant Cofficients. (2D4 +…

A:

Q: 2x³y' = y(y² + 3x?)

A:

Q: Find the solution to the differential equation y' = 2xy? which satisfies the initial condition y(2)…

A: Given query is to find the solution of the differential equation.

Q: If we use the method of variation of parameters, the particular solution of the following…

A: I have given solution in step2

Q: Find the solution to the Cauchy-Euler differential equation xy' +3y'+y=0.

A: The Cauchy-Euler differential equation of second order can be written in the form:…

Q: Verify that the function y = Ce5x is a solution of the differential equation           y′ = 5y

A: The given function is  y = Ce5x  The differential equation is y′ = 5y

Q: (D – 3D + 2) y = (1+ e-")?

A: I am attaching image so that you understand each and every step.

Q: y' = y + y3

A:

Q: y = Ax² + Be*

A:

Q: y' = (4x + y)²

A:

Q: The ordinary differential equation 2xy" + y = ycosx is linear False O True

A: Given differential equation is 2xy'' + y = ycos(x)

Q: Solve the differential equation with the given initial condition. y' = y – e2ty4, y(0) = 1

A:

Q: Find the general solution of the differential equation: y" – 2y - 3y= - 3te. Fi: of the…

A:

Q: Find every nonzero solution of the differential equation y = y +2y°.

A:

Q: Determine the general solution to the given differential equation by using the annihilator…

A: Given differential equation: y''-2y'+y=x3+4x The auxiliary equation is given by:…

Q: Match the differential equation with its solution. y' - 4x'y = x3 %3D

A:

Q: Verify that the function y = Ciex + C2e2x is a solution of the differential equation y" – 3y' + 2y =…

A: Given, second order differential equation y''-3y'+2y=0 To verify that y=C1ex + C2e2x is a solution…

Q: verify that given situation is solution of the differential equation. y' + 4xy = 0, y = 25e−2x2

A:

Q: find the general solution of the first-order linear differential equation. xy' + y = x

A:

Q: Find the solution of the Linear Homogenous Differential Equation Cofficients. D²(D + 2)*y = 0 =D(

A:

Q: Find the solution of the Linear Homogenous Differential Equation with Constant Cofficients. (D² –…

A:

Q: Use the method of annihilators to determine the general solution of the nonhomogeneous linear…

A:

Q: Find the general solution of the differential equation y – e³x+y = 0 using separation of variables.…

A:

Q: 2xydx – (y² – x²)dy = 0 ; x= 4, y = 0

A: Note the following exact differential equation : x dy+y dx=dxy 2xy dx+x2dy=dx2y .

Q: . The standard form of the first order linear differential equation x y'+xy +2 = 0 is,

A: This question is based on to form a standard first order differential equation.

Q: = Form the differential equation by eliminating arbitrary constants : y = ax +0x , .3

A:

Q: Verify that y = (x³ – x) In cx satisfies the differential equation (x³ – x)y' – (3x² – 1)y = x5 –…

A:

Q: Find the solution to the differential equation dz 3te3z dt %3D

A:

Q: Use a substitution to solve the nonlinear differential equation: (y + 1)y" = (y ')²

A: Let y' = t Then , y''=dtdy  to find the value of y, integrate y' =t⇒∫dy =∫t. dt⇒      y =t22  So the…

Q: What are two linearly independentsolutions of the differential equation y''-5y'-6y=0

A: We have to find linearly independent solutions of the given differential equation.

Q: Find the general solution of the given second-order differential equation. 5y" + y = 0

A: To solve the given differential equation.

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.