For what value of x will the curve y = x3 – 3x2 + 4 be concave upward?

Q: 1. y = c1e-2x + cze²x + cze2x 2. y = c1e* + cze3x

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Q: Given the solution:  y = C1e-2x + C2e2x + x2  Which differential equation is it a solution of?

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Q: Which of the options is the differential equation that accepts the solution of the following…

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Q: Find a differential equation whose general solution is y = C₁e6t + c₂e-4t y" - 2 y' - 24 = 0 X

A: The solution of the DE is: y=c1e6t+c2e-4t where the solutions to the auxiliary equation are 6 &…

Q: For the differential equation x-4y"-2y'+y 0, the point x = -2 is Select the correct answer.

A: One distinguishes the following cases: Point a is an ordinary point when functions p1(x) and p0(x)…

Q: If y = x2 – 2x and x changes from 2 to 2.01, find ∆y. (SOLVE BY USING DIFFERENTIAL EQUATIONS)

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Q: Q2/ Solve the differential equation by using the appropriate method y' = (y + 4x)² %3D

A: 2 Given differential equation is y'=y+4x2......1. We have to find the general solution of the given…

Q: Q2/ Solve the differential equation by using the appropriate method y' = (y + 4x)2

A: Formulas of the differentiation and integration ddxxn=nxn-1∫xndx=xn+1n+1+C∫1x2+a2dx=1atan-1xa+C

Q: y = ce2t + Cze -3t y = ce-t/2 + cze¯ -2t

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Q: Determine whether the function y = x3 is a solution of the differential equation 2xy′ + 4y = 10x3 .

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Q: Find a differential equation whose general solution is y = c₁e³t+c₂e-3t 5t = 0

A: The general solution,y=c1e5t+c2e-3t

Q: Q2/ Solve the differential equation by using the appropriate method y' = (x + y – 5)²

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Q: ~2 _ dar,ך3-א 3זר) ד2?ו? .מ

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Q: Find a differential equation whose general solution is y = c₁e³t+c₂e-2t 2 = 0

A: We need to determine a differential equation corresponding to the general solution: y=c1e5t+c2e-2t.

Q: Q4: solve Bernoulli differential equation t2 y'--2ty+y3 ?

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Q: What will be the order of the differential equation if its solution is y=Acos7x-Bsin7x a. None of…

A: Homogeneous Linear Differential Equation with Constant Coefficients: A homogeneous linear…

Q: dy Q-2. Solve the differential equation by direct method dr 1³ + 9x² + 27x+ 27

A: Given differential equation dydx=1x3+9x2+27x+27 It can be written as dydx=1x+33 ⇒dy=1x+33dx…

Q: What is the general solution of the differential equation 2xyy' y? - 2x³ ?

A: We have to find the general solution of the given differential equation 2xyy'=y2-2x3 .

Q: Q2: Solve the High order differential equation by using Operator Method y(4) – 6y" 5x

A: Here the auxiliary equation is m4 - 6m3 = 0

Q: 4. Solve (D² -1)y=(x² +2x² + x +6)e²* using differential operators method.

A: Given D2-1y=x3+2x2+x+6e2x

Q: (b) Find the complete solution of the differential equation y" + 9y = -5x² + 4cos2x

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Q: What is the solution of the following differential equation that satisfies y (1) = 7 and y '(2) = 3?…

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Q: Find a differential equation whose general solution is y = c₁est + c₂e-2¹. 5t = 0

A: I have given the answer in the next step. Hope you understand that

Q: Solve the differential equation using the Method of Undetermined Coefficient. Show your solution.…

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Q: Find the differential equation whose general solution is y=c1e4t+c2e-5t

A: Find the differential equation of given solution.

Q: Q2: Solve the High order differential equation by using Operator Method y(4) – 6y"" 5x

A: We have to solve the given problem by operator method.

Q: If f(x) = x3 + 2x, find f”(2).

A: The given function is f(x)=x3+2x.  To find f''(2)

Q: Find the general solution for the differential equation. y' = 2 - x³ + x6

A: Given query is to find the solution of the differential equation.

Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

A: we can find the particular solution.

Q: What is the degree of the differential equation dy = 5a4 – dr3 6x2 ? |

A: Clearly the exponent of (dy/dx) is 3.

Q: What is the solution of the differential equation of (2x° + ry? + 2y +3) dr + (x²y + 2x) dy = 0 ?

A: We have given differential equation,   Differential equation is of the form,     Mdx +Ndy=0 Firstly…

Q: Find a differential equation whose general solution is 7t y = c₁e¹t + c₂e-2t. y" - 5 y' - 14 y = 0 ✓

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Q: Solve (D² – 1) y =(x³ +2x² +x +6)e²* using differential operators method.

A: Differential equation.

Q: 2x³y' = y(y² + 3x²)

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Q: Find the general explicit solution to the differential equation y′ − 3x2y = x2

A: The given differential equation is y'-3x2y =x2. We solve the differential equation by separation of…

Q: For which value of the constant c is the function y = 15e-® + x + c a solution of the differential…

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Q: Find the general solution of the differential equation y′ = 1/ x√(4x2 − 9)

A: To find the general solution of the differential equation y'=1x4x2-9

Q: s, p°+ 3 xp²- yp²-3xyp = 0 find the differential equation

A: Given: p3+3p2−y3p2−3y3p=0 The standard notation for p is p=dydx.

Q: y(4) – 8y" + 16y = (3x – 5)e²- solve the differential equation

A: Consider the given equation,

Q: Solve the differential equation by variable separable method dy (1+ y) (3x² + 6) = 2- dr 13 + 6z

A: To find- Solve the differential equation by variable separable method dydx = 21 + y23x2 + 6x3 + 6x

Q: Find the particular solution to the differential equations,Evaluate the polynimial by finding the…

A: Given that: xdy+ydx+xy(3dx+dy)=0x=-3 and y=9

Q: At what point of the curve y = x3 + 3x are the values of y’ and y” equal? (SOLVE BY USING…

A: This is a basic derivative problem where we need to satisfy the given condition

Q: Find the complete solution of the differential equation d²y Ap 4- + 13y = 2x2 +5

A: Given differential equation is d2ydx2-4dydx+13y=2x2+5       1 Auxiliary equation corresponding to…

Q: What is the differential equation of the solution: y = C1e3x + C2e-5x + C3e7x

A: Given query is to find differential equation of the solution.

Q: Solve the differential equation (D² – 8D + 16)y = -3e4x by an %3D appropriate method.

A: Given: D2-8D+16y=-3e4x The auxiliary equation is: m2-8m+16=0 Now solve;…

Q: What is the solution of the differential equation y' + 6y + 25y = 64e-3 ? %3D

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Q: (D² – 2D + 5) y = 25x² + 12

A: Given: D2-2D+5y=25x2+12 So,  The auxiliary equation is: m2-2m+5=0 Now solve; m2-2m+5=0m1,…