The solution of the following linear equation xy' + 2y = x² – x +1 is: a. y = --- 3 b.y = c.y =-+ + HIN

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: Ans: (x + y)e+y = C y'+--2

A: Given differential equation is homogeneous differential equation which can be solved by converting…

Q: find general solutions (for x>0) of the Euler equation x3y3  -3x2y"+xy'= 0

A:

Q: Consider the differential equation d²x dx + b. + cx = 0, dt (9.4.5) di2 where b and c are constants.

A:

Q: Find the general solution of the DE (2y – x2) dx + (y+2x) dx=0 А) 2ху + 3 y2 =C 2 (в) 2ху — 3 x3 y2…

A:

Q: The solution interval of 2y +12≥3 or 3y 1 or y≤ -1} .B O (-∞, -1]U (1, ∞ ).CO {yly ≥1 or y<-1} DO

A: We have to find the solution interval of  2y + 1 ≥ 3 or 3y &lt; -3

Q: 1. Determine the roots of the following simultaneous nonlinear equations using multiple-equation…

A: For the given  initial guesses  x0= 0, y0 =1 5x2-y2=2 5x-2y2=-6

Q: 1. Find the general/particular solution of the following linear equation at first order. a. x²dy -…

A: Given : The following are the three linear equation of 1st order a  x2dy-sin2xdx+3xydx=0b…

Q: Obtain two linearly independent solutions valid near x = 0 x2y" + x(x-1)y' + (1-x)y = 0

A:

Q: Solve the second-order equation y" + 2y' – 3y = 9x with initial condition y(0) = 0, y' (0) = 0.

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: x(1-х)у" - Зу' + 2у %3D0

A:

Q: Obtain the solution of the following differential equations. 3. (16x + 5y)dx + (3x + y)dy = 0 ; the…

A:

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

A:

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

A:

Q: х' %3D —х +у— 8 y = y' = 3x + y – 4t

A: We need to find the solution to the following system of differential equations.…

Q: Find the general solution for the homogenous equation of y′′ − y′ − y = 0.

A:

Q: value of c in the equation: dV/dt = -500 (t+1)-2, when  V=700and t=0 is

A: follow next step

Q: y" – 2y' + y = –3 – x + x²,

A:

Q: If the root of an auxiliary are rı = 2+3i and r2 2-3i, the differential equation is %3D Select one:…

A: We will find out the required differential equations for given roots of auxiliary equation.

Q: x°y" – 3x'y"+ 6xy'– 6y = 0 -

A:

Q: find general solutions (for x&gt;0) of the Euler equation x3y3 +3x2y"+xy'= 0

A:

Q: Find the general solution of the lines Зу + 2 y - 2 )dx + ( 2x -+ 1 )dy = 0 4 2

A: Let us consider the given differential equation f(x,y)dx+g(x,y)dy=0 Using substitution,  x=X+hy=Y+k…

Q: 2. Obtain the general solution of the following equations: (i) x²uxx + 2xyuxy + y²uyy + xyux + y² uy…

A: If you want I solved other option please post it again

Q: The solution of the differential cquation y+2ry =3.2y when y(1)=3.2 is

A: The solution is given below in the next step:

Q: Which of the following systems is equivalent to the differential equation y" + 9y" = cos(x) – y? 9uz…

A:

Q: 22 To solve y =cy - by' change to u= 1/y?. Substitute for y in um - 2yly³ to find a linear equation…

A:

Q: Find that solution of y’= 2(2x-y) which passes through the point (0,1). Use Linear Equation of Order…

A:

Q: Determine the roots of the simultaneous nonlinear equations (x-4)^2 + (y-4)^2 = 5 x^2 + y^2 = 16…

A:

Q: Find two linearly independent solutions of y" + 3ry = 0 of the form Y1 = 1+ a3x³ + a6x® + · .. Y2 =…

A: We find two linearly independent solutions of the given differential equation  y"+3xy=0.......(1)

Q: Find the solution of the following system of differential equation: x' = -x + y – 8 у'3 3х + у — 4t

A:

Q: What is the differential equation of the family of lines whose sum of the intercepts is fixed as k ?…

A: Given:  What is the differential equation of the family of lines whose sum of the intercepts is…

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

A:

Q: Solve the following system of differential equations: Y2 = 2y2 + y1 ; yi = 2y1 + 4y2 yı(0) = -4 ,…

A: The given differential equation can be written as:y2'=2y2+y1y1'=2y1+4y2y1'=2y1+4y2⇒D−2y1−4y2=0…

Q: 5. = y – xy³e-2x у —

A:

Q: If y and y, are solutions of a non-homogenous equation y" + ay + by =c then y,-Y2 is a solution of…

A:

Q: find a second independent solution of the given equation.…

A: Rewrite the given differential equation, in the form Divide the given differential equation with x2…

Q: Solve for the 2nd order nonhomogeneous linear equation: y"+12y'+37y=10e-4t     ; y(0)=4,  y'(0)=0

A:

Q: Find the Particular Solution indicated. (Homogenous Linear Equation with Constant Coeffiecients)

A: Given : Homogenous Linear Differential Equation with Constant Coefficients               D2+D-12y=0…

Q: Find the solution of the following system of differential equation: x' = -x+y – 8 y' = 3x + y – 4t

A:

Q: What is the general solution of the following differential solution? y" – 2y – 15y = -5e² O cjet +…

A:

Q: 2xy y' + 2x² x' = y² x'

A: Given: 2xyy' + 2x3x' = y2x' ⇒2xydy + 2x3dx = y2dx ⇒2xydy- y2dx=- 2x3dx

Q: y +y² – 1 = 0, Yı = 1

A:

Q: Given the differential equation 4ry + 6x) dr + (r³ – 6x²y² – 1) dy = 0 ,What is (3z y 6M by %3D -- O…

A: Given:       3x2y-4xy3+6xdx+x3-6x2y2-1dy=0 Here M=3x2y-4xy3+6x            N=x3-6x2y2-1

Q: Find the solution to the linear of differential equations 42x + 120y system satisfying the — 15х —…

A:

Q: Solve the system of the linear differential equations! メニムメーリ 4'= 2x+ 3y with initial condition…

A:

Q: 3. Find the general solutions of, dy_x+y dx х-у, а.

A: given differential equation is  dydx=x+yx-y

Q: Solve the given system of differential equations by systematic elimination. (D + 1)x + (D - 1)y - 5…

A: Step:-1 Given system is D+1x +D-1y=5  ----(1)6x +D+5 y =-1  ----(2) To solve this system multiply…

Q: x²y" – 4xy'+6y= 0, y(2)= 0, y'(2)= 4 %3D -

A: Given differential equation is: x2y''-4xy'+6y=0           y(2)=0; y'(2)=4 In Cauchy Euler method we…