Show that the general cubic equation y3 + by2 + cy + d = 0can be transformed into an equation of the form x3 + px + q = 0by using the substitution y = x - b3

Q: Solve by "ref with back substitution 2x+3y-4z=1 x+3y=4 y-z=0

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Q: Give the general solution to the equation x' Ax where A = %3D

A: To find the general solution of the given system, first we find the eigenvalues and corresponding…

Q: Find the number of non negative solutions to x+y+z= 21. With the conditions that x < 3, y ≥ 2, z ≥…

A: Given that x+y+z=21 with the conditions x&lt;3, y≥2, z≥4

Q: 4. Show that the equation x² + y? + z2 - – 2z + 6y + 4x + 15 = 0 represent a point.

A: our objective is to prove.

Q: Find the solution of 2y-y² sec²(xy²) + (2x − 2xysec² (xy²))y' = 0 given y(1) = 2.

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Q: Solve second order DE  16y"-8y'+5y= 0

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Q: If y, and y, are solutions of a non-homogenous equation y" + ay' + by = c , then y, - y2 is a…

A: Since y1 and y2 are two solutions of the non-homogeneous equation, we have y1''+ay1'+by1=c…

Q: - Reduce the equation x2 + y2 - 5xy + 8x- 20y + 15 = 0 to the standard form. %3D

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Q: show that the 2x2-y2=C is a solution to yy'-2x=0.

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Q: Čonvert the following equation into standard form. 7x y = - - 3 %3D 2 [?]x+ [ ]y = [ ]

A: The given equation is y=-7x2-3

Q: Which is the best approximation to a solution of the equation In (x + 3) = 2x+ 2? %3D

A: Here we have to find the solution to the equation ln(x+3)=2x+2 using the graph.

Q: D. y" + y’ - 3y = 4sin 2x

A: This question is related to differential equations, We will solve it using given information.

Q: Determine the roots of the equations using iterative methods with initial values of 1. 2x + 6y + 3z…

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Q: Find the homogenous linear equations of the following. y = 3e2xsin(3x)

A: Follow next step

Q: 3. 31 √ √(²x- (2x - 4y)dydx 1 -1

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Q: Use undetermined coefficients to find the particular solution to y''−4y=2e^−3t

A: Use undetermined coefficients to find the particular solution toy''−4y=2e^−3t

Q: discuss the nature of the quadratic equation form  x2+4xy+6xz-y2+2yz+4z2

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Q: Verify that x and x* are solutions to x²y" – 6xy' + 12y on (0, 0), and give the general solution to…

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Q: Give the general solution to the equation x' Ax where A %3D %3D 3

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Q: Show that the equation x+y+z=4,2x+5y-2z=3,x+7y-7z=5 are not constant

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Q: Solve for x: xy2 + yz2 - 4 = 2x - 1. 3-yz2 b) х %3D у2-2 a) x = *y^tyz2-3 2 с) х %3D 3 — yz2 -у? +2…

A: Consider the given expression.

Q: 5. Use the method of undetermined coefficients to solve (a) y" +2y' + y = x²e¬ª.

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Q: quadratic form 1.) 2xy+6xz-4yz 2.)x2+y2+z2+2xy

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Q: x' = -3x + 2y, y' = -3x + 4y; x (0) = 0, y(0) = 2 %3D %3D

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Q: Write down all of the product solutions satisfying: и +иу —D 0, 0 <x<2, 0<у<1. %3D u(х,0) — 0, и,…

A: Note:- As per our guidelines, We’ll answer the first question since the exact one wasn’t specified.…

Q: Find a particular solution to y" + 7y' + 10y = -19te“. %3D

A: Introduction: When there is a non-zero function of the independent variable on the right-hand side…

Q: 1. (1-х)у' %3D у?

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

A: We have to verify if the given is a solution to given differential equation or not.

Q: The equation y3 = 3Bx is the general solution of 3y Oy Oy 3xy Ou' = 3y

A: We will form the differential equation using given solution

Q: How to create cubic equation (y=ax^3+bx^2+cx+d) using the points (0,0), (1,1) and (2,4)

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Q: Find a particular equation for the DE: y+4y'-2y= 2x -3x+6

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Q: 2x + 3)y’ = y + (2x + 3)1/2

A: Given differential equation can be reduced in linear differential equation

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: Find the general solution of 2y"+3y+y=3sin.x+xe"

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Q: Show that the equation 2/x– 1– Vx = 3 has a solution.

A: Equation is 2x-1-x3=3

Q: 4. The Quadratic equation whose roots are 1 and %. c. 2x-3x+1-0 a. 2x +x- 1- 0 b. 2x-3x -1 0 d. 2x…

A: Hello, thanks for the question. We’ll answer the first question since the exact one wasn’t…

Q: Solve the nonhomogeneous equation: (D2-4)y = 2 –8x, when x=0, y=0, y’=5, using undetermined…

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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: Verify that for x>0, (2/ /3)x³² 2 is a solution of the equation yy" =x.

A: Given:     To verify: y is the solution of equation yy''=x

Q: Find the solution of y' = (1 – 4x) y², y (0) = –1 in explicit form

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Q: Show complete solution. 6y^2dx-x(2x^3+y)dy=0

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Q: List the roots of the auxiliary equation for a homogeneous linear equation with real  constant…

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Q: Find the general solution of each nonhomogeneous equation. 1. y" + 4y= 8

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Find a particular solution to y" + 4y + 3y = 3te". %3D

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Q: the general solution of the inhomogeneous equation y '' = 9x 2 + 2x -1

A: Given: y''=9x2+2x−1