Find the general solution of the folowing ODE: dy -3x² e¯4y dx x³ + C y = - 4 y =In(**÷C) 4 y =1n(x³ +C) e y = 41 n (x³ +C)

Q: Q9/ find the integration ſe^( (2x) ^3-1) x2 dx? * 1 а- 6. e2x* -1+c 1 b- e2x3 +C 1 .2x3–1+

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Q: df Use integration to find f(4) if- dx O 42.667 O 43.667 O 47.667 O 48.667 = 2x² and f(0) = 5.

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Q: Evaluate L 8y (x³ + 1)² 2y by reversing the order of integration. dady

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Q: Find fæxyzz for f(x, y, z) = z³y² ln(x). [Show your solution.] Select one: O O O x² 6z²y x² 2z³y x²…

A: See this solution in below.

Q: Find the antiderivative of 5sinx In 5 cos x dx. A.) 5cosx + C B.) 5sinx + C C.) 5sinx In 5 + C 5sin…

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Q: (2xy + x? + x+)dx – (1 + x?)dy = 0 -

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Q: Determine | An (x) An+1(x) dx, from the relation: tn .1 Σ (2n + 1)! tn+1 A, (x) An+1(x) dx n=0 n -1

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Q: Q6) Compute the integral 3 1 dxp -з (х +2)3

A: Here we solve the given integral.

Q: Evaluate the integral 2 dx where fx) if -2 s xs 0 16-2 if 0xs3

A: Given function is The integral isThe integral can be written as: Plugging the function and applying…

Q: Solve using product rule d(uv) = u dv + v du: f(x) = (3x^2 – x + 4) (2x^2 – 1)

A: Our Aim is to solve the given function using the Product Rule where f(x)=(3x2-x+4)(2x2-1)

Q: What is the general solution of the following ODE y' - (2y/x) = 3x3 Hint: Use integration factor…

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Q: Use the modified Euler Method to solve the ODE = subject to y 1 when x 0 %3D dx 1+x on the interval…

A: To find y(0.3) by using the modified Euler's method.

Q: Use chain rule to find express answer in terms of x only. dx y = Vu² – 1 u = 4Vx

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Q: Evaluate the integral. 2+e-2x dx e3x 10 +C O -2e-5x(5e3x + 1) + C e Sx(10e2x + 3) + c 15 1 e 3* 2e2x…

A: The given integral is ∫2+e-2xe3xdx. Evaluate as follows.…

Q: The function y = 0 is always a solution to a linear homogeneous ODE. Select one: O True O False

A: A Homogenous linear differential equation isa differential equation in which every term isof the…

Q: sume that w = and f (x) = e . Find and dt ds II II

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Q: Write the following expression as one integral. 5 7 5 I from S₁ •Sf(x) dx - - f(x) dx + - f(x) dx -7…

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Q: Solve the ODE by y Integration a. = 0

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Q: Evaluate by USing first Substitution and then partial Prachons TF necessary. 3x dx .3x e

A: We have to integrate above function by substitution and then by using partiap fraction Please see…

Q: D(D² + 9)y = sin3x - 5

A: Using method of linear differential equation with constant coefficient.

Q: Find the general solution of the ODE below. 2z y'" – 4y' + 4y = e" arcta y(x) =

A: Introduction: If a second-order homogeneous differential equation has two equal real roots, then the…

Q: Find the derivVative of the function. 5. y= In 8v +5 dy dv %3D

A: The objective is to find the derivative of the function.

Q: 2. Find the integral 2x+3 dx x2-9 a. In/(x – 3)³(x + 3) + C а. b. In[(x – 3)³(x + 3)] +C c. 2ln[(x –…

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Q: Find the -of the following function : ду w = cos (x2 + 2 y) – e4x- z*y + y3 .A a w = 2 sin ( x2 + 2…

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Q: Evaluate the integral. 3x-7 (a) S- dx x2-2x-8

A: Answer and explanation is given below..

Q: y" +Zy+3y=sin (3x)

A: Given that,  y''+2y'+3y=sin(3x) The auxiliary equation is m2+2m+3=0m=-2±4-122=-2±2i22=-1±i2…

Q: Let Dx be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: Solution: Consider the given linear transformation : Dxf = 2x + 3 Since D is the linear…

Q: Let Dx be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: We have to solve above question and find preimage function

Q: Choose the letter of the correct answe. 1) x² (xdy + ydx) = (5- xy) dx a) x ln (5-xy) = 1- cx b) -x…

A: We are allow to solve first question only .If you need rest of answer please upload it separately…

Q: dy + 3y = 0, y(0) = 7 dx

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Q: Q3. Use the inverse operator method to solve the nonhomogeneous ODE for its general solution y" –…

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Q: Evaluate the integral Зx2 — 4х — 9 A В + C dx using x3 – 2x2 – 9x + 18 - 2 x +3 – 3* х — х — 3x2 –…

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Q: 4- 13 + 6y = 0 dx

A: We have to be find

Q: f y=y(x) is the desired solution of 2 = f(x,y), Derive Euler %3D teration formula for solving ODES…

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Q: df Find dx by using chain rule if f = u =-1 , x=-1 u+1

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Q: Find fy if f(x, y, z)=1-2xy²z+x²y yxy B) -4z O A) 4z O C) -4 O

A: Sol

Q: Find the antiderivative of 5$sinx ln 5 cos x dx. A.) 5cosx + C B.) 5sinx + C C.) 5sinx In 5 + C 5sin…

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Q: dy 2. Find the general solution to the ODE dx 3x %3D x + 1

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Q: df Use integration to find f(4), if = dx O -26.667 O -19.667 O 26.667 O 30.333 5x2, and f(1) = 7.

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Q: a) Use the definitlon of derlvative to find ds If dt 2t+1

A: As per bartleby guideline for more than one question asked only first is to be answered please…

Q: Is the function 3Sin26x a special function of the operator d? /dx? ?

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Q: Find the general solution of the ODE. d'y dy +3. dx² dx Stre

A: Given d2ydx2+3dydx=5x+xex

Q: Q9. Find y2 using Reduction of Order y" – 3.ry +4y = 0, Yı 1 = x?

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Q: 2. Show whether the ODE is exact and find and use an integrating factor if needed. (x² + y²)dx - 2xy…

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Q: Identify the Bernoulli's equation of first order ODE. а. dy +10xy = y sin x dx ,3 b. dy +10x²y = sin…

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Q: of of For the function f(x,y) = In (x+ 3y), find and dx df of ду II

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Q: Find f(x) dx where f(x) = Į(x - 3)e¯× 0 sx< 2 2 sx s3 1- 72x-3 Enter an integer or a fully reduced…

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Q: Q1-Evaluate the integral 2х — 5 dx - х2 — 5х + 1 3

A: Here I am attaching image so that you understand each and every step.

Q: ntegrais. I, da, D= {(x.y) 0sxs20sys2% dA, D = x +2 [['e"d4, D={(x,y)| 0s ys 4,0sx<y}

A: Double integration

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.