1. a) Find , if y= (x² – 11)“ dx b) Express (8/30) (2Z60) in the form a+ bi c) Solve (2+3) +3/- x+iy d) Evaluate (1+54(2-2)

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

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Q: Find 2 and z if z is defined implicitly by the equation ду x² + 2xyz + y° + e² = ln 4

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Q: Q7. Solve the Cauchy-Euler equation (i) 4.x²y" + 4.xy' – y = 0. (ii) 4x²y" + y = 0.

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Q: use the Lagrangian method to solve:   U=(x+3)(y+5) given 30=3x+2y

A: Given the relation 30=3x+2y. We need to minimize the value of U = (x+3)(y+5). Substitute the value…

Q: the solution of the homogenous equation (хусот х -)dy - Ydx = o

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Q: Q6. Use the method of Variation of parameters to solve (i) y" + y = tan x. (ii) x²u"+xy' +(x² – !)u…

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Q: 5. Show that 1 T = VI? + y? satisfies the equation Tz + Tyy = T3

A: Given T(x,y)=1x2+y2

Q: Find the roots of the cubic equation x3-3x- 4 Ocorrect to 2 decimal points using Newton-Raphson…

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Q: 4. (D² + 2D + 5)y = 4e-*cos²x

A: Given differential equation is: d2ydx2+2dydx+5y=4e-xcos2x Auxiliary equation corresponding to given…

Q: 5. Solve xdx + ydy а? (хdу-ydx) x2+y2 using exact D.E method.

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Q: 2. Solve by: a) Fixed point, b) Newton-Raphson, and c) Secant methods: xex – 2 = 0 For a) and b),…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: ?The Third Equation for i3 7in+12i3-=-3-O 5i1+12i3=0- Zir-4i2+16i3=-3- 0

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Q: Determine exact solutions for the equation 2sin2x-3sinx + 1 = 0 in the interval x e [T, 3n].

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Q: 6z dy (78)a

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Q: a) Find the general solution of the equation dªy dy dx² 4- x2 + 3e* - dr4 by using the method of…

A: As you have posted multiple parts,but they are independent so according to our guidelines we will…

Q: Q5. A. Solve the Euler-Cauchy equation xy - 4xy + 6y = 0

A: The given questions are four individual questions. As per bartleby expert policy, only one…

Q: Verify that y, = e2x and y2 = e5×are solutions of у" - 7у' + 10у %3D 0

A: We have to verify that the functions y1=e2x and y2=e5x are solutions to the given differential…

Q: - Find the solution of the equation 3U, -5U, = 0 satisfying the condition U(0, y) = sin y

A: We have to find the solution to the given equation.

Q: 1nd the general and definite solutions of the diIference equations

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Q: Find the general solution of the equation xy' = ky that is valid for x > 0.

A: We have to find y(x) for this equation which is valid for x>0. We use integration to solve this…

Q: c(x, 1) = exp solves ac(x.1) a'cx.1) at

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Q: 3. Find the general solutions of, x+y dx x-y, a.

A: We have to solve the given differential equation.

Q: Solve. a) y - e" cosy b) +2y= + 2y 6e **-+(Let u - )

A: Since you have asked multiple subparts of this question, we will solve the first three subparts…

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

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Q: x°y" – 3x'y"+ 6xy'– 6y = 0 -

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

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Q: Use undetermined coefficients to find the particular solution to y'' – y' – by = 3e* Y,(t) =|

A: The given differential equation is  y"-y'-6y=3e3t  We have to find the particular solution of the…

Q: 9. Solve for y, showing all work: 12x – 4y = 20

A: Using algebraic operation

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

A: Given differential equation is dydx=-8xy2+4x4x+1y-8x3+4x2-1             …(1) y=x is a solution of…

Q: 1. Solve for the othogonal trasctories y =x²(1-cx)

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Q: Q1. (4 marks) Find the general solution of the Cauchy-Euler equation: x²y" – 3ry + y = x°, r>0.

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Q: a. Find that solution of y' = 2(2x-y) which passes through the point (0, 1). %3D

A: For part a). Given that                      y' = 2(2x-y) =4x-2y                      y' + 2y = 4x…

Q: 1. Solve the following Cauchy-Euler equation. x*y" – 4xy' + 6y = 2x* + x?

A: To solve the below Cauchy-Euler equation. x2y''−4xy'+6y=2x4+x2

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

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Q: 2. 2 Solve (D² +2DD' + D'² -- 2D– 2D')z =sin(x +2y)

A: Given the pde

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: (4) B/ If Ø = (x³y²z) and A = 2xz 1-3y2j+ 3xy²k Find ?у ?х the point (2, -1, 3)? at

A: Given:        ϕ=x3y2z         A=2xzi^-3y2j^+3xy2k^         ϕA=x3y2z2xzi^-3y2j^+3xy2k^…

Q: Use undetermined coefficients to find the particular solution to y''−9y'+20y=−1768sin(t)

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

A: Given Cauchy-Euler differential equation is

Q: 5 solve the 1UP: y% 4y(2)+ 3y'= Y1)=e+ % ,uG) = et %

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Q: 5. Give the graphical significance of the constant a for the equations of the form y-a(x-h)²+k.

A: We have to discuss the graphical significance of given equation.

Q: Solve by making the appropriate substitution

A: Given equation

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: Apply the appropriate method to solve the Cauchy-Euler equation 2x²y "+ 5xy'+ y = x² – x

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Q: 2. Determine the general solution of y(") = x- 2y cot (2x)

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Q: 1. Solve the equation on the interval 0s0<2x. 4sin 2e-3=0 O A. 3'3 元 5元 B. 6 6 I 5x 7 11x С. 6 6 t…

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Q: 3. Use the Intermediate Value Theorem to show that the following equation has a solution. sec(x) =…

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Q: 7)Starting with x1=1, find the 3r" approximation x3 to the root of the equation x' +2x + 4 = 0

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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.