A. When reduced to a linear DE of order one in z, the Bernoulli's equation B. + z(+)=-3x² C. dz +2(-1)=3x² +2(-4)=3x² D. + 2(2)=3x² dz dy C. dz = dx dz dy + z(-¹)=-3x² homogenous of smallest degree? dw dy SE with t + y()=3x²y² becomes dx

Q: Eliminate the constant: 2x 3x =c₂₁e²x + c₁₂e³x Oy"-y'-6y=0 Oy"-5y'+6y=0 Oy"+y'-6y=0 Oy"+ 5y'+6y=0

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Q: 5. At each point (x, y) on a continuous curve, the slope of the curve is 6xy. If the curve contains…

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Q: y(6) – 4y®) +6y® - 4y'+y =7

A: Answer

Q: C.1. Give a real general solution to the equation u'''' - 5u''' -6u'' = 0 :

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Q: The Bernoulli equation y'+37 xy'= 34 y can be converted to one of the following linear equations: a.…

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Q: 2. The amount of heat H (in joules) required to convert one gram of water into vapor is linearly…

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Q: Write down two linearly independent solutions of the Bessel equation 16x?y" + 16ry + (162 – 9) y =…

A: The given differentiate equation can be written as:

Q: -. Find an equation of line L. (1,3) (-3, –1),

A: We know that slopem of line which passes through pointsx1,y1,x2,y2 is given by m=y2-y1x2-x1…

Q: Find two linearly independent solutions of y" + 1xy = 0 of the form Y₁ = 1+ a3x³ + α6x6 +.. Y₂ = x +…

A: The given problem is to find the coefficients of the 2 linearly independent solutions for the given…

Q: Which of the following is the general form of a homogenous equation? A a, (x)y"…

A: The objective of the question is choose the correct option.

Q: Solve by reduction of order. Find y2 and y (x² + 1)y" – 2xy' + 2y = 0 yı = x -

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Q: 11. In the function y = 3x2 - 3, y is replaced by y and then y is replaced with y +2 ; the new…

A: Given:     Function y=3x2-3   Here y is replaced by 12y       substitute y=12y      12y=3x2-3…

Q: 4. Determine constants a, b, c, d and e that will produce a quadratic formula Lf(x)dx = af(-1) +…

A: Given that,  To hold for polynomials Plugging these into the formula.…

Q: What are the roots of the auxiliary equation for a homogeneous linear equation with real, constant…

A: We have to solve the problem

Q: How to solve this equation y'''-4y''+2y'-8y=6e^(x) - x^(2) + 1 using Methods of Undetermined…

A: Given: Given differential equation is y'''-4y''+2y'-8y=6ex-x2+1 We will solve this equation using…

Q: 2. (LI-2) Consider the equation r2y" - xy + y = 0. It is given that y₁ = z is one solution to this…

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Q: If e* and xex are solutions of y"tay'tby=- Are soluhons linearly independent? write the soluhion.…

A: Given that e−x and xe−x are the solutions of y''+ay'+by=0. We have to check whether the e−x and xe−x…

Q: For the difference equation given by y(k + 1) + y(k) = 3 (1/2)* with y(0) = 1 Find the expression of…

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Q: If r2+ 2r –1 = 0 is the characteristic equation of a homogeneous D.E. with constant coefficients,…

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Q: 3. 2хydx - (3xу + 2y?)dy %3D0 o (x - 2y)*(2x +y) = c O (x - y)*(x + y) = c (х + 2y)(2x - у)*- с о…

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Q: 2.c) Eliminate the Arbitrary Constants in the equation: * y – x = C1e* + Cze-2* -y" - y + 2y - 2x +…

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Q: 8. (a) For f(x) = Vx, give the linearization at a = 25. (b) Use your answer from part a to approxi-…

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Q: 3. Find how many roots the equation 2z4 – 323 + 3z² – z + 1 = 0 - - has in the right half-plane Rez…

A: Given: 2z4-3z3+3z2-z+1=0

Q: y" - (y") = 0 denkleminin çözümü aşağıdakilerden hangisidir? %3D O a. y = +(2z + c1)2 + czz + C3 %3D…

A: subtitute y'=v where v is the function of t v''=V'3 v=2it+c1+c2 y'=2it+c1+C2 y=c2t+c3+i22c1+t3/23…

Q: The differential operator (D2 - 16D+113)³ annihilates the functions

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Q: 2xy y' + 2x² x' = y² x'

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

Q: What is the image of (4,-1)(4,−1) after a reflection over the line y=xy=x?

A: Reflection over y=x means:  (x,y)→(y,x)  We need to find reflection of (4,-1) over y=x line .