5. In solving a linear first order ordinary differential equation, show that the solution remains the same when using e P(x)dx+c_instead of just el P(x)dx as an integrating factor for the equation dy + P(x)y = Q(x) dx

Q: 2. x²y' – 2xy = x* + 3; y = 2 when x = 1

A:

Q: Find the particular solution that satisfies the initial condition: Differential equation: 2xy' - ln…

A:

Q: Find the general solution of seperable differential equation dy/dx=x3y2

A:

Q: 4. Show that both x₁ (t) = et cost and x2(t) = et sint are solutions to the second-order…

A: To show that both x1t=e-t cos t, and  x2t=e-t sin tare solutions to the second‐order differential…

Q: Create a third order, non-linear Ordinary Differential Equation with enough initial values to be…

A:

Q: 4. The standard form of the first order linear differential equation x'y'+xy + 2 = 0 is

A:

Q: 6. Given a differential equation with coefficients linear in two variables. If the DE represents…

A:

Q: 3. Show that the differential equation dx is homogenous. Zxy

A:

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: Suppose that y1 = e x and y2 = e −x are the solution of a homogenous linear differential…

A:

Q: The diffeterctial equation is y²dx+ 3xZy² dx + dy=0

A: In the given question we have to find the value of the constant c at the point (2,1) when we solve…

Q: (4) a general solution of the 4th-order differential equation y +y(3) + y" = 0.

A:

Q: Find a linear differential equation with constant coefficients satisfied by e2x, e-x, e3x and e6x

A:

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: 5. By using separable differential equation, solve the initial-value problem 2x(y + 1)dx -y dy= 0,…

A:

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

A:

Q: use the method of variation of parameters to find a particular solution of the given differential…

A:

Q: ex 2. y" — 2у' + у %3 1+ x2

A:

Q: Find a linear differential equation with constant coefficients satisfied by e² ³x, and e4x

A: A linear differential equation having auxiliary roots m1, m2, m3,....... have following independent…

Q: Find the general solution of xy' + y = y2lnx Bernoulli's differential equation.

A:

Q: One solution of the differential equation y''+y'=0 is y=e^-x. A second linearly independent solution…

A: We will find out the required solution.

Q: 3. Show that the differential equation (1 – 2y + x In a)dx + (e2v – 2x)dy = 0 is exact and find its…

A:

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

A: We have to verify the solution

Q: 5. The differential equation (3x'e' - 2xx+ (r'e' -sin y ldy = 0 is exact because ON

A: Partial differentiation is needed to be done after identifying M and N

Q: 2. Use variation of parameters to determine the general solution of the nonhomogeneous linear…

A:

Q: 2. What can you say about a solution of the equation y' = -25y2 just by looking at the differential…

A: Firstly we integrates, then solve it.

Q: If Yi - 2cosinx and ya-2 sin lnx are two solutions of a second linear differential equation. Then…

A: We use the definition of the Wronskian to answer the given question.

Q: 5. xdy = (y + 2x³)dx

A:

Q: Excrcise 1: 1. Let the following higher order differential equation (1) y/" – 2 y" – 3 y = 3e.…

A: For higher order differential equation,           Let  P0xyn +P1xyn-1+.........+Pnxy =F(x) .....(A)…

Q: Determine the appropriate form for yp on the differential equation y" = 9x^2 + 2x - 1 %3D

A:

Q: The General solution of differential equation def ined by: 2x² y " – x y'+y=0 is defined by y(x) =…

A: Solving Cauchy Euler differential equation

Q: 4 By using separable variable method, find the general solution of the differential equation dy _y…

A:

Q: 9. What is the particular solution of the linear differential equation ,3 Y = x° – 2xy; when x = 1,…

A:

Q: 3. Show that the differential equation zxy

A:

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

A:

Q: 1) (y = 1

A: As per our guideline we can solve maximum one question you can repost other questions

Q: 2. Find the particular solution for the dy differential equation dx = 2xy and y = 3 when x = 0

A: We will find the particular solution of the differential equation , dy/ dx  = 2xy   .

Q: Write down a linear homogenous differential equation (with the smallest order and constant…

A:

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

A:

Q: Find the general solution of the first-order differential equation                       y cos x −…

A: Given: y-1cosx+dydx=0 for finding solution of given differential equation, we use variable separable…

Q: The solution of the differential equation by variable separable method dy (1+ y²) (3x² + 6) 5- is dx…

A:

Q: 3. The Bernoulli's form of the differential equation x³ydx+(3x¹-y³dy=0 is

A:

Q: 8. The differential equation (2x' -xy² -2y+3dx-(x'y+ 2x)dy =0 is exact because ON

A: Given:     Differential equation 2x3-xy2-2y+3dx-x2y+2xdy=0 The differential equation is exact if…

Q: y" – 2y' + y = -3 - x+x².

A:

Q: 5. In the differential equation 2rydx + (y² -xy-0. what is -- 心

A: Solution

Q: Find the particular solution to the differential equation: dy/dx=3x^2cos^2y. Solution passes…

A: The given differential equation is in variable separable form. We solve the differential equation by…

Q: Find the particular solution to the differential equation y′ = 4x + 3 passing through the point…

A: To find: y'=4x+3dydx-4x=3       dydx+Py=Qwhere P and Q are variables of x onlyI.F.(Integrating…

Q: If the differential equation +8. + 9x = m dt2 is overdamped, the range of values form is? Your…

A: Let the differential equation is,                       ad2xdt2 +bdxdt +cx =0 .............(1) It…

Q: Solve Bernoulli differential equation of y + ry = ry².

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.