4. Is (1,5) a solution of 3x-2y S-4

Q: Which of the following is a particular solution of the equation y"+y'+7y=4cos2x? O a.…

A:

Q: Is (2, –1, 3) a solution of 3x + 5y – 2z = -5 2х + Зу- z 3D —2 2x + 4y + 6z 18? Replace x with 2, y…

A: Consider the system of equations. 3x+5y-2z=-52x+3y-z=-22x+4y+6z=18 And, the solution of the system…

Q: 22:- Solve the following Equations by Gauss - Jordan method 2X+4Y-6Z=-4 X+ 5Y+3Z=10 X+3Y+2Z = 5

A: Here we have to solve the equation by using the Gauss-Jordan method.  2X+4Y-6Z=-4X+5Y+3Z=10X+3Y+2Z=5…

Q: General Solution of xdy-ydx=x2exdx is

A: We know that for the differential equation of the form  dydx + P(x) y = Q(x) the integrating factor…

Q: 4 (a) s(-) = -2x + -4x +3x (b) s(<) = 2x° + (c) s(2) = -2(x - 2) (*+ 4) %3D 2.

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Q: What is the solution of 3x2 + 6xy2 + (6x2y + 4y2 ) y' = 0

A:

Q: a) By using Naïve Gauss Elimination. 2x + 4y – 2z = 0 x- y = 2 x + y+ 2z = 4

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Q: What is the particular solution for y′=−2e^x−3x^2+x−4 such that y(0)=1?

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Q: 2. Determine the complete solution of xydy – (x + 2y)²dy = 0 %3D

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Q: Give a particular solution for y" – 2y' + y = 3e*.

A:

Q: 7. Solve for x, y and z using Gauss-Jordan Elimination 2w + x – 3y – 3z = 4 x + 2y +z = -3 2w – x +…

A:

Q: What is the particular solution for y′=6e^x+x^2−7x such that y(0)=6?

A: Given problem:- y'= 6ex+x2-7x  Particular solution for given differential equation when y(0) =6

Q: Let (xp, y,) be the solution of the following equations In 2 (2x)™² = (3y)n3 3Inx = 2lny %3D Then xo

A: Given equations are 2xln2=3yln33lnx=2lny

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

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Q: A) (:: :) Verify that y = c₁cos(3x) + c₂sin(3x) is a solution of y' +9y = 0

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: 4- Find the particular solution for: 3x²y' = 5x – 6xy, x = 2 when y = 1 %3D

A:

Q: Find the general solution of 2xy^2 + 4 = 2[3 - (x^2)(y)ly. (x^2)(у^2) + 4x - бу 3D С (x^2)(y^2) + 4x…

A: Tip: if you couldn't solve the differential equation, differentiate the given option and check which…

Q: 10. Particular solution of y"-4y' + 8y = x³, when x = 0, y = 2, y' = 4

A: We have to find the particular solution of y''-4y'+8y=x3,  when x=0, y=2, y'=4.

Q: A) S(x)=- у-аxis 4. 3. X-axis .6 -5 4 3 -2 -1 4. -2 -3 -n of unis O fx)= *-2x-3 x-2 у-аxis 64 х-аxis…

A: Given the two functions: 1. f(x)=x-2x2-12.f(x)=x2-2x-3x-2 We need to sketch the graph and find the…

Q: 4) Find the general solution of the 2nd order PDE 2и. - Зи,, +4и, 3D10 6) +** s (3x +2y) answer:

A: Given : 2nd order PDE       2uxx-3uxy+4ux=10                 --------- (1) To find : general…

Q: 4. Find for the particular solution of y' = x3 – 2xy when x = 1, y = 2 %3D

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Q: Find a particular solution to y″+36y = 60sin(6t).

A:

Q: 3. Verify that 3e-2x +4e* is a solution of y"- 3y' + 2y = 0.

A: We have to verify that 3e-2x+4ex is a solution of y'''-3y'+2y=0

Q: 1. Determine all possible solutions of ²u ex² = d²u oy ² by using variable separable method. 7

A: The given problem is to solve the given partial differential equation by using the method of…

Q: Find a particular solution to y" + 6/ + 9y = 3.5e 3. Yp =

A: Given thay  y"+6y'+9y=3.5e^(-3t) To fin the particular solution

Q: 4 Find the general Solution of the following PDES • з Их + 2 Иу -Х u(x,c) =4е 2 (зу-2х)12 ans3- и(x,…

A:

Q: 1. Find the solution of the IVP; 3y" – 11y' = 2x³ – 5x + 1 + 4y %3| - - y(0) = –1. %3D y'(0) = -2…

A: Given initial value problem is  3y''-11y'-4y=2x3-5x+1 with y0=-1; y'0=-2. Consider the homogeneous…

Q: 4. Find the solution of the following DE: a. y(5) + 5y(4) + 10y(3) + 10y" + 5y' + y = 0

A: Given differential equation is: y5+5y(4)+10y(3)+10y''+5y'+y=0 Write auxiliary equation corresponding…

Q: Show that the equation 2³ + 3y3 = 923 has no solution in integers, other than x = y = z = 0.

A: Suppose that, x3+3y3=9z2 has a non-trivial solution, that is other than (0,0,0), and minimal.

Q: Find a particular solution to y′′+36y=60sin(6t) yp=

A: The given differential equation is  To calculate the particular integral let us consider If we put…

Q: 10. Particular solution of y" – 64y = 16, when x = 0, y = 1, y' = 0 %3D

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Q: If ů = (1, 4t, 2t-6)dt, then | |P= 0. V3 9. 3

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Q: 5. What is the particular solution of " 2xyn = 1+y, when a 2, y = 3 y = V5x – 1 y = V3x + 2 O Option…

A: If (x,y) is a solution point of a differential equation, then the solution point must satisfy the…

Q: The equation X2 - 19Y² = 13 has an integral solution, i.e., there is a pair hat x2 19y2= 13. (proof…

A: We have to solve given problems:

Q: 1. Show that y = c,x1 + c,x³ is a family of solutions of x?y" - xy' - 3y = 0.

A:

Q: Find the general solution to the homogenous DE y'-16у' + 64у %3 0

A: The given homogeneous DE is y''-16y'+64y=0. The auxiliary equation is m2-16m+64=0.

Q: Find a particular solution to 16.5e-2t t2 +1 y" + 4y' + 4y Yp =

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Q: Solve the inizial Nalve pooblem 2xe %3D yco)3=

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Q: 2y + 4y + 4z 3z = 0 w + = 7 w + 3x + 7y + 2x 92 = 4 4y 6z = 6 - -

A:

Q: What is the particular solution of 2xyy' = 1+y2 , when x =2, y = 3

A: The given differential equation is solved below in detail.

Q: 3. Find the general solution of the following DE. y' = 3 (y + 1) O y = ce³x - 1 3y = ce³x - 1 Oy =…

A: Use variable separable to Solve this problem.

Q: What is the particular solution of (3y2 + 10zy²) dz + (6zy 2+ 10y) dy = 0 when a = 1 and y 2 ? Sry +…

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Q: b) Find particular solution of х*у 3- (х-1) у. У(1) — 1. У(1) %3D 1.

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Q: Find the general solution. 6y(4) + 7y" – 12y" – 3y' + 2y = 0 SHOW WORK.

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Q: Give a particular solution for y" – 2y' + y = 3e*

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Q: 1- If y+3y = 8 then g- solution is %3D a- y + 6 = 1 b- In (8-3y) =x + c 3 a

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Q: 5+ 12x2 - 4x xdx a (2x? -3)/5+12x² – 4xª + 14in/2x² - 3+/5+12x? – 4x*|} b H2x2-3)/5+12x² – 4x +…

A: To evaluate the given integral.∫5+12x2-4x4 x dx

Q: 4) Prove that y = x-3/2 is a solution to 4x2y" + 12xy' + 3y = 0.

A: