1. Let y = r3 –- 2x² +1 and z =r² – 1. Find de when z = 3. Please first write down the formula and then get to the calculations. -I.

Q: Let y(x) be the solution for the DE: y = (x + y-1)? If y(0)– 1, then find y() 3元 O 2+7 O8-7 O 2-7

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Q: xarctanydx + dy = 0 2(1+ y²)

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Q: Solve the given DE y'= X - x 3 — 2y 3 3ху 2

A: We have to solve the differential equation

Q: For the equation Mdx+Ndy=0, if both M and N follows that f(Ax,\y)=^k f(x,y), the equation is A.…

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Q: Solve the following D-E 2) + xy = 6x/y %3D

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Q: Suppose Q ssnes equation dQ -0.07Q. dt Assuming that Q + 0, what does this tell you about the values…

A: dQ/dt = -0.07Q dQ/Q = -0.07dt Integrate both sides ,we get Ln(Q) = -0.07t Q= e^(-0.07)t Here…

Q: Which of the following is a solution to xy" + y' = 0 ? y = = 1 y = x3-x O A y = In x %| O D В

A: A function y = f(x) is said to be solution of the given equation  xy" + y' = 0  ...(1) if  y = f(x)…

Q: 4. For the DE y"-3y' x+3e", write the solution of the homogenous equation y., then write a…

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

Q: Let y(x) be the solution for the DE : y' = (x + y – 1)² If y(0) = 1, then find y()

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Q: If C = 100, k = 0.1, and t is time in minutes, how long will it take a hot cup of coffee to cool to…

A: From Newton’s Law of Cooling, we know that T(t) = Ts + Cekt Given C = 100, k = 0.1 Consider freshly…

Q: te Use an appropriate substitution to solve 2yy+ r? + y? +x =0.

A: The solution is given as

Q: A series RL circuit with R = 50 2 and L = 10 H has a constant voltage V= 100 V applied at t = 0 by…

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Q: Solve the DE y'=(x+y+2)^2, y(0)=2 by setting u=x+y+2.

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Q: Let y(x) be the solution for the DE : y = (x + y + 2)2 If y(0) = -2, then find y() ○2-푸 O 8 - T O -…

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Q: Solve (x² + 4)y' = 2xy In|x] = In(y? + 4) +C O Option 1 Inlyl = In(x² + 4) +C

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Q: Consider the following IVP: y"+a?y = 0; y(0) = 1, y'(0) = 0 Find the general solution.

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Q: 3. Solve the DE ty' + 2y = ont, 4. Solve dy dr 1+ y?

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Q: 1. 3(3x² + y²)dx – 2xydy = 0 -

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Q: b) Now, start with the exact same equation as before, i.e. Vz+ Vj= 5,

A: Given  x^(1/2) + y^(1/2) =5

Q: 2. Find the general solution of d'y d'y + 12 dr Sy 21e dr

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Q: Find the general solution to y" – y' – 2y = 3x + 4. (Be sure to find the values of the coefficients…

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Q: b, y" -zy'-3y= e*

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Q: Solve for for the equation y = aln(x + )+ 4tan(;)– 2x O a. T O b. In(4 + x) O c. none of these O d.…

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Q: II. Solve the following DEs by LT. 2. y" – 3y" + 3v' – y = x²e*, y(0) = 1, y'(0) = 2, y"(0) = 3

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Q: Let y(x) be the solution for the DE: y (x + y +2)² If y(0) = -2, then find y() 7- 3 4 2+ O 8 JTO 3…

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Q: Solve the following difference equation with initial conditions: 12Yn + Yn+1 = Yn+2, Y₁ = −2, Y₂ =…

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Q: Suppose that the DE y"" (x) + 7y(x) =70 2³ +123 has a solution of the form y = Az³ + B Find the…

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Q: - The particular solution (when x = 1, y 0) of cosy xe + 6^-4 dx- y dy 0 4+ has the form Ae* + Bx? +…

A: We will find out the required values.

Q: C - S N. L Solve for C: V = C - -

A: Given equation is: V=C-C-SLN We have to solve for C.

Q: 2. Solve the following DE x y" – 4y = x e

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Q: Q1) Solve the following DEs а) ty" + (1 — 2t)y' + (t - 1)у %3D 0 y1 = et

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Q: Solve the following DE: 1. (D² – 3D + 2 ) y = 4x?

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

Q: solve the following D.E ,t<3 y" – 3y - 4y =- , y(0) = 0, y'(0) = 0 : ,t23

A: Here we will use Laplace transform method to solve the given differential equation.

Q: If e-x, xe-x are the solutions of y''+ay'+by=0 then, what are the values of a and b.

A: To find- If e-x, xe-x are the solutions of y'' + ay' + by = 0 then, what are the values of a and b.

Q: 1. Find the general solution of the equation By - ty 11 y t

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Q: We have determined that y = 1 and x = 52. Substituting these expressions into the third equation…

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Q: Solve for X and Y in the simultaneous equations below;   S^2X+SX+SY=S S^2Y+SY-4SX=-S

A: for the value of X and Y ,solve the given two equation ....

Q: Solve for x and y:                                     ax + by = a – b and bx – ay = a + b

A: given:

Q: 1. Solve the following equation: а. yy" + 2y' = (y')² 9y" + 6y' + y = e¯(2 – 4x + 4x?) b.

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Q: dy 4) 2xy = x² + y? + 1

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Q: 4. Find the solution for the following y""+y"+ 2y = 3 y(0)= 1, y(0)=1,y)=1

A: Solution :-

Q: Solve the following DEs: 1. 4y" + 16y' + 17y = 0, when y = 1, x = 0; y = 0, x = n

A: Note: As per bartleby instruction when more than one question is given only one has to be answered.…

Q: Solve the following IVP. 2y" + y' + 2y = g(t), y(0) = 0, y'(0) = 0 where 5 st< 20, g(t) = 0 st< 5…

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Q: z Solve the following di fferential equations xdy y x²+y² 1. dy

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Q: Solve for y. P(0)=(-12/37, y), P(0) is in Ql

A: Given P(θ)=-1237, y and P(θ) is in Quadrant 2.

Q: Solve the following DE: (2xy + 3x²) dæ + (2xy+ 4y) dy = 0 O a²y? + x³ + 2x?y? + 4y3 - 2xy = C O a'y?…

A: Solving the given differential equation

Q: 4. Which is an equivalent form of the following equation? 2x-3y 3 Oy=--1 Oy=x-1 Oy=r-1 Oy=3x-1

A: Please refer the attached image for complete solution.

Q: Explain how to solve the below equation step by step:    T = { m E Z | m = 1 + (-1)^i, for some…

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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.