1. Find the general solution. а. (3х — 2у + 1) dx + (3x — 2у + 3) dy — 0 Ь. dy/dx 3D (9х + 4у + 1)? c. 2x'y' = y(y² + 3x²) using Bernoulli.

Q: Q3 /Write Only the (Order and Degree) of the following differential equations a) (d'y/dx')24 -…

A: Use the definition of order and degree of Differential equation.

Q: 2. Solve the general solution for the First Order Linear DE. удх %3D (еУ + 2ху — 2х)dy

A:

Q: Solve the following 2nd order differential equations: d²y 2 dx2 dy (i) 11 + 12y = 3x – 2 dx - d²y 2…

A: Given differential equation is: 2y''-11y'+12y=3x-2 Auxiliary equation corresponding to differential…

Q: Find the non-homogeneous equation of the 2md order D.E. y + ỹ– 2y = -5x³ + 2x mogeneous equation of…

A:

Q: Solve the following non-homogeneous Differential equation using reducible to homogeneous method. 1)…

A: According to our company guidelines we are supposed to answer only one question, since you have…

Q: Ql- Find y(2.1), x(2.1) for the following first-order simultaneous differential equations by…

A:

Q: 1. Find the general solution of: du dx _ _ y + xy² + x³ x+x²y+y² dy

A:

Q: Find the solution of the differential equation (D° + 8D³ + 16D)y = 0 у %3D С, + (С, + C;x)сos y = C,…

A:

Q: Find a differential equation for y=c1e^9t +c2e^-4t. Oy"+5y'+36y=0 Oy"-5y'-16y=0 Oy"-5y'-36y=0…

A:

Q: (1) 3 dy + y = dx 3 Find the general solution to: 1. -

A:

Q: 2. The differential equation (4x'y -6xy-2x-3dx + (2x*y – 2.x' kdy = 0 is exact because ƏM ON dy

A:

Q: Find the particular solution : y" + y' + 16y = cos4x (a) yp = -4sin4x Yp =sin4x (b) %3D %3D (c) yp =…

A: The correct option is b i.e. yp=14sin4x i.e. 14sin4x is the particular solution of the differential…

Q: Find a particular solution of the equation y2y' = cosx satisfying the initial condition y(0) = 0.…

A:

Q: The differential equation (1- z) (dy - dz)- 2rydx for y (0) = 1 can be transformed to a standard %3D…

A: Try to put all dx term and dy term together.

Q: 1. Find the general solution of dy dx + y = x

A:

Q: Find the general solution of dy xy = 1+ y?

A:

Q: Suppose we are given y₁ (x) and y2(x) (with y₁ y2), which are two different solutions of a…

A:

Q: 3. Solve the Bernoulli DE: 5 dy - 5y : dx | - 2

A:

Q: Find the solution to the Bernoulli equation. y = 2(3x+ y)2 – 1; x= 0,y=1 O 4tan-1(3x+ y) = 8x + T…

A: The solution is given as

Q: 7. Obtain the solution of (D² – 4)y = 16 + cos 2x using the method of undetermined coefficients %3D

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find the general solution of (y + 1)dx + (4x - y) dy = 0 Show your solutions on a separate sheet of…

A:

Q: 6. What is the general solution of the following differential a²ycdy d²y dx2 dy equation -5 +4y=0)(4…

A: Given differential equations are, d2ydx2-5dydx+4y=04d2ydx2+6dydx+2y=0 Solve the equation by solving…

Q: 2. Find the general solution of d²y dy +5- dr.² dx 6y=0

A:

Q: Solve of the following system of differential equations: (z' = 2x + y, %3D ¤(0) = 0, y(0) = 1. (y' =…

A: Given system of differential equations is x'=2x+y and y'=-14x+y with the initial conditions x0=0 and…

Q: Find the particular solution of the differential D2+4D+3x=e-3t, given that t=0, x=12 and dxdt=-2

A:

Q: 1. Find the general solution of dy dx +y=x

A:

Q: Q4: Find the general solution of d?y dy - 3 - 4y 3e2t + 2sin t - 8et cos 2t, dt dy y(0) = 2, (0) %3…

A: Given that  The differential equation  To find the general solution

Q: the solution to the IVP(x2+y2)dy/dx+xy=0 with y(0)=2 is

A: Given DE is x2+y2dydx+xy=0  and y(0)=2 find the solution of the DE

Q: Find the general solution of y"-3 y'+2y = e2* [using variation of parameters] cos x

A:

Q: 4. Find the solution of (x²+6y²)dx – 4xydy=0 when x=1, y=1. Use Substitution Method.

A:

Q: 8) Find the general and particular solution for the following separable equation dy -.5y, y(0) = 2…

A:

Q: 3. Solve the problem y(t) – y(t) = 4t with initial condition y(0) behavior of the solution as t → o…

A:

Q: Find an explicit solution to the initial value problem dy/dx = 2xy +3y, y(0) = -2

A:

Q: 2:- A. Solve the following differential equations using variation of parameter Method: Mads) d²y 1.…

A:

Q: - Second order : non- homogeneous Equations with Constant Coefficients d²y 4-- + 16y = 10 cos 4x dx²

A:

Q: 7. Solve the following Cauchy-Euler equation d’y dx² dy +5x- +3y = In x. dx

A:

Q: Solve the homogenous diff equation of; xdx . (y+1) dy y³ e-x = 0

A:

Q: Obtain the general solution of the following differential equations. 4. x(x² + y*)*(ydx -xdy)+y°dy =…

A: We have given differential equation ,  xx2 + y22ydx - xdy + y6dy = 0 Clearly , this is homogenous…

Q: Which of the following most nearly gives the differential equation for all parabolas with vertex on…

A:

Q: The differential equation for y = Ae3 + Be9r is: %3D o y'+12y'+27y=0 o y'-12y'+27y=0 o y"-12y'-27y=0…

A: Differentiate given equation twice w r to x

Q: (2xy +y) dx + (x²- x ) dy = 0

A: Given: (2xy+y)dx+(x2-x)dy=0, y(0)=e

Q: 4. Find the general solution of y"- 4y – 12y = 5le sin(3r).

A: To find - Find the general solution of y'' - 4y' - 12y = 51exsin3x

Q: A- solve = x + y² with condition y (0) = 1, x o= 0 to x =0.2 and h = 0. by Rung kutta dx method 4th

A: The given differential equation is dydx=x+y2 with conditions y0=1, x0=0 to x=0.2 and h=0.1.

Q: (b) d²y dy Find the solution for cos(x) ² − (1 + x²) dx − 2xy = 12 with the conditions - dx² dx 1+x²…

A: Given cosxd2ydx2-1+x2dydx-2xy=11+x2y1=-1, y2=2, h=0.25`

Q: d²y + 9y = 2 cos(3x); y(0) = 0; y'(0) = %3D dx² 3

A: Given differential equation is The associated auxiliary equation is Complementary function of…

Q: Find a differential equation for y=c1e^9t +c2e^-4t. Oy"+5y'+16y=0 Oy"-5y'-16y=0 Oy"+5y'+36y=0…

A: Find DE

Q: Find the general solution of the given DE (x-3y-1)dx-(x-3y+5)dy%3D0.

A:

Q: E 2.4. Determine the differential x² + y² + 2ax + 2by +

A:

Q: Find the general solution of (x + y) cos ydr + (a cos y - sin y)dy = 0. |3|

A: Differential Equation: A differential equation is an equation that contains one or more terms and…

Q: 4. Find the solution of the following set of simultaneous equations by ' conditions y(0) = x(0) = 0…

A: