If V1, V2 are two independent solutions of y" + p(t)y' + q(t)y = 0 then Select one: а. V1V2 - Vi'v2 O b. V2 w(V1.V2)V2 w(y1.V2) V1 d.

Q: Solve for the particular solution of the non-homogeneous DE. y'' + y = 2x

A: Solve for the particular solution of the non-homogeneous DE. y'' + y = 2x

Q: Solve system of linear DEs  dx/dt+dy/dt+2y+6y=2e^t 2dx/dt+3dy/dt+3x+8y=-1

A: To solve dxdt+dydt+2x+6y=2et2dxdt+3dydt+3x+8y=-1

Q: Obtain the general solution valid near the origin: х(х-2)y1+2(х-1)у - 2у %3D0

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Q: y" + y = 2x

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Q: Explain particular solution of the forced system                     x'' = Ax + F0 cos wt

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Q: Solve: dy 6- y") +. onn 13-1 Ordineiy Dibgerential equation

A: The solution of the differential equation can be found with the help of the separation of the…

Q: Use variation of parameters to find a general solution: y(3) – 4y = et.

A: Given differential equation: y3-4y'=et         ...(1)

Q: Obtain the general solution valid near the origin: x(x − 2)y" + 2(x − 1)y' − 2y = 0

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Q: y" + y = 2x

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Q: a) 2xy dx+(1+x²)dy=0 b) y'+(4/x)y=x* ------by exact method ---by linear method

A:

Q: 3. Is y(x) = Cisin2x + C2cos2x, where Ci and C2 are arbitrary constants, a solution of y" + 4y = 0?…

A: Given, y''+4y=0 a second order differential equation. To show that y(x) = C1 sin 2x + C2 cos 2x is a…

Q: Solve by Graphical Method Max z=2x+4y Subjected to 3x+4y0

A:

Q: 3. Obtain two linearly independent solutions valid near the origin: 3xy" +(2-x)y' - 2y = 0

A: As per the question we are given the following second order ODE : 3xy’’ + (2-x)y’ - 2y = 0 And we…

Q: 3. Use your solution from Part 2 to give solutions to the IVPS i. y" + 2y' + 16y = cos 3t, y(0) =…

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Q: Use the Adam-Bashforth method of the second order to solve the second equation y’=y(x+y) when h=0.1…

A: Given differential equation is y'=y(x+y), step size h=0.1 with initial condition y(0)=1 Let x0=0,…

Q: use Separation of Variables to find the general solution. yy' = x

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Q: Obtain 2 linearly independent solutions valid near the origin for x>0 2хy" + 5(1 — 2х)у' — 5у %3D 0.…

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Q: y" - 5y' = x - 2, when x = 0, y = 0, y' = 2

A: We have to solve the given differential equation.

Q: Is y(x) = C1sin2x + C2cos2x, where C1 and C2 are arbitrary constants, a solution of y” + 4y = 0?

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Q: What is the general solution of xydx−(x2+3y2)dy=0

A: Topic :- Differential equation

Q: Obtain the general solution valid near the origin: 8x^2y" + 10xy' − (1 + x)y = 0

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Q: 10. y"" + y" = 3 А. 3 В. Зх C. D. 3x?

A:

Q: Y, = Ax² is particular solution of y' + y" = 1 for A = %3D

A: Here, yp=Ax2yp'=2Axyp''=2Ayp'''=0

Q: Find the general solution of the 2nd order non-homogeneous DE using variation of parameters: y” -…

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Q: Find general solution to Cauchy-Euler equation: (t^2)y''-2ty'-3y=t^2

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Q: Show that y = - In x + 3x - 5 is a solution of y" -=0. Use y = - Inx+3x – 5 to find y' and y". y' =O

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Q: 1- , L, v² e*dydx 2- S S マーーー ydxdzdy a>0

A: Explanation of the solution is given below...

Q: Obtain the particular solution. y' = x exp(y-x²) ; when x = 0 , y = 0.

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Q: Find a particular solution to æ' = -x – y + e', y' = 2x + y – ešt using undetermined coefficients.

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Q: Find all equilibrium points for the system 1) x"+(x')* + 2x =0 x' = sin y 2) And y' = e"- -1

A: For the system of differential equation x'=f(x,y)y'=g(x,y) equilibrium points are given by the…

Q: b. Solve by using variable separation method. = 0 ax2' ay2 Which satisfies the conditions, u(0, y) =…

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Q: Obtain two linearly independent solutions valid near x = 0 x(1-x)y" - 3y' + 2y = 0

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Q: Consider the nonlinear system of equations 22 – 3y = 4, 4x – y = 4. (2,-4), one step of Newton's…

A: f1=x2-3y-4=0f2=-y2+4x-4=0 J1,1=∂f1∂x=2x    J1,2=∂f1∂y=-3J2,1=∂f2∂x=4      J2,2=∂f2∂y=-2y…

Q: If integration using u-substitution technique is used to solve for O u = e4x Ou=1-e¹ O U= u = €²x…

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Q: Obtain two linearly independent solutions valid near x = 0  x(1 - x)y" - 3y' + 2y = 0

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Q: X' : 0 1 X + sec t tan t) -

A: Given

Q: Obtain the general solution valid near the origin: 2y" + 9ху' — З6у %3D 0

A: Power series solution of the differential equation

Q: y" = 4

A:

Q: Solve for the general solution xydx - (x² +2y² ) dy = 0 x² = 4y° In(2 ) xy = 4y° In() Option 1…

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Q: Solve for x,y,z if x+ 2y + 2z=0 2x + y + 2z = 0 2x + 2y + z = 0

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Q: Solve the Cauchy-Euler equation: x*y' Зху + 4y = 0. %3D

A: Given Cauchy-Euler differential equation is

Q: Verify that y = 1/(x+ C) is a solution to y'= -y², where C is some constant. Find the particular…

A: Given that: y=1(x+C)

Q: Find the particular solution of xy' – 2y = -x ; when x y = 5 1,

A: Recall: Consider the first differential equation                           dydx +P(x) y =Q(x)…

Q: Solve the DE using Linear First Oder Method: y +yx = x - 3. if y(0) = 2 %3D

A: Given y'+yx=x-3   if y0=2 To find the general solution

Q: az (b) Solve and ди by applying chain rule if z = In(x² – 2y), and x = u + v, y = e". dv

A:

Q: 2- Solve this system of two equations using appropriate numerical method: y = cos' x x² +y° - x = 2

A: Using Newton Raphson method for multivariables.

Q: y +y² – 1 = 0, Yı = 1

A:

Q: 2. Obtain the particular solution. y"-y'-6y=0; when x=0, y=2,y'=1

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Q: Obtain the general solution valid near the origin: x(х — 2)у" + 2 (х — 1)у' — 2у 3D0

A: The differential equation has singularity at the origin. So we find the solution by Frobienius…

Q: Use variation of parameters to obtain the general solution. y''+4y = 4 sec2x

A: The given differential equation is; y"+4y=4sec2x.

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.