IV.Given: A(x) = 5x? - (2a - 1)x + 1 B(x) = 18x2 - 36 %3D C(x) = 5x(x – 3)(x + 1)² %3D 1) Find a, such that -2 is a solution of A(x). 2) Find the roots of B (x) and C(x).

Q: Solve the equation using Jacobi's Method (Error≈0.001): 2x1 - x2 + x3 = -1 x1 + 2x2 - x3 = 6 x1 -…

A: Given system of equation 2x1 - x2 + x3 = -1 x1 + 2x2 - x3 = 6 x1 - x2 + 2x3 = -1

Q: 2D² +3D– 2)y = 0

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Q: Find the general solution of each ff Higher-order DE using Reduction of Order  1. (2D2 + 3D -2)y=0

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Q: Q2: Given the equations 5x,- 4x,+ 3.x; =-19 %3D -lx,+ x, + 2x; =-3 3x, +4x;+ 2x, = 20 (a) Solve for…

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Q: A. Find the general solution of the DE: y" - 2y' +y = 6e'

A: Given A. y"-2y'+y=6et

Q: Find a particular solution, y,(x), of y(ª – y" = 12e3 – 5x + 2. -

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Q: Q4: Use undetermined coefficient annihilator approach to solve. y"" – 5y" + 6y' = 10x² – 5x – 6 +…

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Q: Find the solution by using Solution of 2nd order D-Es 2 X ý XỨ ty - xy + y = Lnx -

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Q: Given that y,(x) = e<* is a solution of y" - y' - 2y = 0, use the Reduction of Order formula to find…

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Q: . Solve the yn+2+4Yn+1-5Yn coefficients = n2"+2" using method of undetermined

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Q: 2 Find the particular solution of y' +y = -x°y5 ; У(-1) %3 2

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Q: Q.4 (A) By using NRM, find the real root of x3 – 2x – 5 = 0 accurate to six decimal places in the…

A: (A) Given: x3-2x-5=0 Differentiate the function with respect to x. ddxf(x)=ddxx3-2x-5f'(x)=3x2-2…

Q: dy = -8xy² dx 3. Solve + 4x(4x+1) y-(8.x² +4x² -1) by knowing u =x is a solution.

A: Given: dydx=-8xy2+4x4x+1y-8x3+4x2-1

Q: Electrical Engineering 2-Show that the method x+1 =Xn 6 + converage to vā. %3D Iegimal I need the…

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Q: To solve for h, first divide both sides by 3x. 3x (x-2) h 3x-3x-33x² +54x 3x 3x (x – 2)h = x - x -…

A: Given: area of the rectangle =3x3+14x2-23x+6also given that width of the rectangle=x+6To obtain :…

Q: Find a second solution to 4x²y" +y = 0, given one solution y1(x) = x!/² In x.

A: Given differential equation 4x2y''+y=0.....1 And given one solution is y1x=x12lnx Equation (1) can…

Q: Find the general solution y" – 6y'+9y=x*e*

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Q: Q(2): Find the general solution of x³y" – 3x²y" + 6ry' – by = xª In x. %3D

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Q: a) Derive the secant method to solve for the roots of f(x)=0 nonlinear equation, b) Use the secant…

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Q: Given that y,(x) = e²^ is a solution of y" - y' - 2y = 0, use the 2x Reduction of Order formula to…

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Q: Q1: Find the general solution of the y - 4y - 5y = 2sin2 x

A: Given differential equation is y''−4y'−5y=2sin2x. We have to find the general solution of the given…

Q: Find the general solution to  y''+ y' = 1 + 2sin(2t)

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Q: determine by inspection at least two solutions of the given first-order IV . 16. xy-  2y, y(0) …

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Q: 2a) find a solution of y" (x) = y(x) that passes the origin and go trhout the point (In(2),-).

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Q: 4. Find for the particular solution of y' = x3 – 2xy when x = 1, y = 2 x2 а у 2e + 2 - ex2 b. y =+…

A: The given differential equation is:y'=x3-2xywhich can be written asdydx+2xy=x3which is a first order…

Q: 5(a) Find the General solution of the Diffe -3x (D² + 6D + 5)y = e 3" (1 – 2sin²x) ||

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

Q: Solve (1- x2)y" +2xy'-2y = 0 on (-1,1) given that y1 = x is a solution.

A: Let us consider the given differential equation P(x) y''+Q(x)y'+R(x)y=0 Then the solution of the…

Q: The equation f(x)= x² -e* has a solution [-1, 1]. With po= -1 p1=1, calculate p2 using the the…

A: The secant method uses the formula: xn+2=xn-f(xn)⋅xn+1-xnf(xn+1)-f(xn) to perform the iteration. The…

Q: a. Obtain the general solution of the following i. (4+x)y'= y³

A: Solve the differential equation using variable separable method. According to Bartleby answering…

Q: Given that y1 = 3x is a solution of æ°y" + xy' - y = x2 on the interval (0, 0), use the reduction of…

A: Concept - used the reduction of order

Q: Use variation of parameters to find yp of x²y" - 2xy' + 2 y = -12 x(1/2) given that yi = x and y2 x2…

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Q: b) Give a particular solution for y" – 2y' + y = et - 1+x2

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Q: 2. Find the general solution of y' = eY(4x – 2). %3D |

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Q: 1. Given the General Solution the DE, Identify the roots * y = C1e4* + C2e¬* + C3 O A) m1= 4; m2= 0…

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Q: y"-y-4e-x+3e2x; y(0) - 0.y(0) --1.y"(0)-2

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Q: 18. Given the equation (x2-4y")(x³yzm-1)= 0, where 0<ns 3, and 0<ms 5 a. What is the highest…

A: Given that  x2 - 4yn (x3 yzm -1) = 0 where 0 &lt; n ≤3; 0&lt;m≤5 To find: a) highest possible degree…

Q: -3 Show that y(x) = -9x7 is a solution to 4x²y" + 12xy' + 3y = 0 for x > 0. %3D

A: We will show in step 2.

Q: determine by inspection at least two solutions of the given first-order IV . 15. y-  3y2/3, y(0) …

A: Consider the given y'=3y23 and y0=0

Q: (2х + 1)у" — 2у - (2х + 3)у %3D (2х + 1)2; У1 —е-*

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Q: (b) Show that for x > 0 and k + 0 the equations In x x* = e* and 1 have the same solutions

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Q: 3. Suppose = f(). (a) Given y(xo)= Yo, when does this equation have a unique solution? (b) Make a…

A: suppose dydx=fymx (a) given yx0=y0, when does this equation have a unique solution? we have  y'=fymx…

Q: - 9y" = 27 %3D

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Q: Find the particular solution to y''-y'+y = 2sin(3x)

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Q: 4. Given that y,(x) = e^ Reduction of Order formula to find a second solution y,(x). is a solution…

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Q: 3- Prove that y=x is a solution of (x³ + 2x?)y"+ 2xy'- 2y = 0 and hence find the general

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Q: Find the particular solution of (2x + 3)y = y + (2x + 3)/2; when x = -1, y = 0 Show your solutions…

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Q: Q2 (a) Determine the solution of y" – y = e2x – x + sin x using method of undetermined coefficient.…

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Q: (g) Any separable equation M(x)+N(y)y' = 0 is also exact. %3D

A: Since you have asked multiple question, we will solve first one for you. If you want other question…