Solve Hhe following by Separcting initial vallue 2006lems g the Variables 1 %3D %3D dx

Q: te ,t<- 3 b) Let y(t)= find L(y(t)) + sint cost 3

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Q: (a) Find the position, velocity, and acceleration when t = 3 sec.

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Q: 4. y(x? + y) dx + x(3x?- 5y) dy 0; x =2, y=1

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

Q: Solve each equation for y. Show all work. a. z - 3(y+ 2) = 6 6x-1 b. 3 = 2 OStep 1 (a): OHint 4 x +1…

A: As per our guidelines we are suppose to solve only first three sub-parts of a question. Kindly…

Q: 9. (x +y) dx – (y – x) dy = 0; y (1) =1 %3D

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Q: AP When the radius r of a sphere increases with time r, the change in volume dt O a. 4 Ob. 4tr dt dr…

A: As we know that the volume of a sphere is : V=43πr3

Q: The number of cars produced when x dollars is spent on labor and y dollars is spent on capital…

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Q: Solve for the particular solution. Please provide a detailed sol'n... Do not shortcut.…

A: Here, the given differential equation is: x+x4+2x2y2+y4dx+y dy=0

Q: The revenue generated by a certain company is approximately related to size of its workforce…

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Q: Find the value the constant a that makes the equation ay?dx + (a + 2)xdy = 0 is an exact.

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Q: . Given dx y + x (a) Solve the equation (b) Verify that your solution in part (a) is an implicit…

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Q: ation yy' = y² +e*. he equation to make it a B

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Q: Use l = PRT to solve. %3D (time is in years) | = $300 P = $3,000 T= 0.5 years Find R. [?]% %3D

A: Given data,I=$300P=$3000T=0.5 yearsFind R?

Q: Identify the type of solution for each problem and solve for the general solution. Choose the most…

A: To identify the type of solution for the given problem and to solve for the general…

Q: 1 2 ху S S xe^ dx dy 0 -1

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Q: Q.41 The value of the quantity P, where P = | xe*dx, is equal to

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Q: (iv). (2ry? + 3a²)dx + (2a²y+4y²)dy = 0 %3D

A: We have to state the order and check it it is exact or not.

Q: (x + xy²)dx +e** ydy = 0

A: Solution: A first-order separable ODE has the form of N(y).y'=M(x)

Q: ,3 e s-axis is s = -t° + 12t- 45t m. elocity is zero. |

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Q: lecessary steps. (a) / = V2r – 1 dz (b) ; dr edr +1

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Q: Solvejẩ gẩjen diffejrẩeẩtiaẩlẩjequation by separation of variables. 12 dx y In x dy + 2y + In|y| = 2

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Q: idy 12 dy + 3 dx 3 dx? ||

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Q: C is jointly proportional to L, W, and H. he given information to find the constant of If L = W = H…

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Q: FTnd the General/Practical solution FoT +he Following DTFFerentiat equation. {x-9x? + 16x - 144)y?dy…

A: The differential equation is given as x3-9x2+16x-144y2dy=2x2-1e4ydx find the general solution.

Q: The number of cars produced when dollars is spent on labor and y dollars is spent on capital…

A: We have to calculate dy/dx

Q: olve the diffrential equation.(pls step bu step and clearly) (d/dx+2x)(dy/dx+2xy)=2e^(-x^2)

A: (d/dx+2x)(dy/dx+2xy)=2e^(-x^2)

Q: Which of the equation(s) are dimensionally compatible? E i. = v2 + 2aAx m iii.F = mv + v² A. all of…

A: Option ' C ' is correct .

Q: t If the velocity of a moving object is v(t) =——- 2/2 in meters per second, then what is its…

A: We know that velocity vt = dsdt, here s is the velocity.

Q: 3) S,(x + 1) e**+2* dx = ? A. B. C. e³ – 1 D. e* - e

A: option (B) is correct  see the calculation below

Q: ing factor of the equation, (r +y° +1) dz (xy+ y) dy = 0, z +1 7 0. (z+ 1) * C. (x + 1)* D. e(z+1) *

A: We have to solve

Q: d²0 de +y dx² 4sinø dy 3.

A: Categorize whether the given equation is PDE or ODE, linear or non linear, degree and order.…

Q: 7. dx = y(1+ y²)sec²x dy

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Q: Q.41 The value of the quantity P, where P = |xe*dx, is equal to

A: To find the value of the quantity P, where P=∫01 xex dx.

Q: Thres Find the Equation of the crcle passing The paint () g haveng eo centae at ,

A: This question is related to geometry and in geometry it si related to circle .the given equation of…

Q: The number of cars produced when a dollars is spent on labor and y dollars is spent on capital…

A: Given problem:-

Q: 3. (x2 + у2 + 1) dy +хydx%3D0

A: "Since you have asked multiple questions, we will solve the first question for you.  If you want…

Q: dy y(ln y – In a + 1) dx

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Q: (2xy-y)dx+x(x+ 1)dy = 0 %3!

A: Exact differential equation :       A differential equation is said to be exact if it satisfies…

Q: 03 (final answer) ( 3x²y + e' )dx + ( x³ + xe' – 2y)dy=0

A: To find out the solution of the differential equation.

Q: у dx + (у өу-ху-2 х) dy

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Q: Determine whether fhe e Xaut . i7 it is exact, solve it. given differental eguation tosk -2kg)…

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Q: Solve the first ODE and find the value ofC constant when y(1) 2 dy 6x + 4x + 4 4y dx Your answer

A: Ordinary differential equations

Q: Given y3 – xy2 – x²y=2. Then, at the point (1,2), is Blank 1 dx Blank 1 Add your answer

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Q: C. Solve the following Bemoull's equation. 2. dx

A: First divide y^9 both sides.

Q: a? +b 7. Find dx where a, b are constants b- ar

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Q: A lighted candle burns outr according to the equation y'(t) =kv (t) where y is the length (in…

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Q: The weight First three months a newborn infant dluring its life Cin pounds of modeled by + +3+…

A: Given: w=13t3+52t2-196t+8.

Q: a dx a+x e

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Q: dy Solve: (e +e-²)- = y? (separation of variables) dx

A: We want to solve the given differential equation.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.