1. 6. dx (x – 3)²dx V1+8x -1 2. 7. 3 x²dx (5– 19– x²) dx 3 1 (1- х3)2 -3 3. 8. 3x 1 1dx -dt t4+t² + 1° 4. 9. x²dx cos*t – sin²t dt | (x + 1)* 10. x2 dx cos(t) + 3 dt x²V4 – x2 5.

Q: Solve the following initial value problem using the undetermined coefficients method: d'y dt2 + y =…

A: Given d2ydx2+y=8cos2x-4sinx with yπ2=-1,  y1π2=0

Q: 2. a) Using Laplace transforms, solve the following first order ordinary differential equation - 2y…

A: Solution:-Step1:-   The given differential equation is                    y'-2y=e2t+sin 3t…

Q: Consider the following initial value problem: x" 5x14x = sin(8t), x(0) = 2, x' (0) = -1. Using X for…

A: In your answer this will be 696 place of 632

Q: Transform the following Bernoulli differential equation of the form 2+ P(x) · y = dx Q(x)y" or +…

A: Note:-Our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 20. Solve the following differential equa- tions using classical methods and the given initial…

A: As per our guideline, we are supposed to solve only first subpart. Kindly repost other subpart as…

Q: slove the initial value problem: (dx/dt)-5x=cos(4t) with x(0)=5 find x(t)

A: The given initial value problem is: dxdt-5x=cos4t with x0=5. The given differential equation is a…

Q: Determine the solution of an initial value problem; 2e°cos2x dx+ (e'sin2x + 3y sec²y²) dy=0, =0 4 A…

A:

Q: 1. Find the differential dy in each of the following. a. y = 2x* – 3x³ – 5x

A:

Q: 1. Solve the initial-boundary value problem du 0 0 3 dx2 u(0, t) = u (4, t) = 0 t 20 37Tx u(x, 0)…

A:

Q: 2. a) Using Laplace transforms, solve the following first order ordinary differential equation y –…

A:

Q: 2. Find the differential dy for each of the following: A. y= x - 2x + 1 +e* B. y=- 2)

A:

Q: 1. Solve the initial-boundary value problem ди 2 a²u 0 0 %3D 3 dx? u(0, t) = u (4, t) = 0 t > 0 %3D…

A: Given initial-boundary value problem    ∂u∂t=23∂2u∂x2,…

Q: 5. The motion of a mass attached to a dashpot and a spring as it experiences a force can be…

A: Given differential equation is  md2xdt2-Bdxdt-kx=1    , m=1, B=1, k=6, x0=0, x'0=0⇒d2xdt2-dxdt-6x=1…

Q: Suppose the same spring-mass system is now attached to a movable plank, which moves like the…

A:

Q: Find the differential equation of the following function (x – 3y + 2)dx + 3(x + 3y – 4)dy = 0 x-1 a.…

A:

Q: 6) Use Laplace transforms to solve the differential equation: dy dx2 dy -7- ·+10y=e2* +20, given…

A:

Q: 1. Solve the following initial value problem: dy xy cos x; dx y(0) = 0.5 %3D Idy =

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Q: 2.1 By applying Newton's second law to a body at a certain distance x at time t, the following…

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Q: 1- Problem 4: B) Estimate the following integration with n = 4 using Trapezoidal rule and find the…

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Q: 1- Solve dx = cos x + y, where y = 2.0 at x 0 take step size h = 4x = 0.1 and solve for 0 ≤ x ≤ 0.2…

A: Given : dydx=cos x+y where y=0.2 at x0 takes step size h=∆x=0.1 To find: Solve for 0≤x≤0.2 using…

Q: The solution of (1 +y²)+ (t- etan-ly- dy =0 is: dt Select one: a. tan-ly C elan-ly b. ce2tan-ly. tan…

A: Given:1+y2+t-etan-1ydydt=0

Q: Find the differential equation of the following function (х — Зу + 2)dx + 3(х + Зу — 4)dy — 0 х-1 a.…

A:

Q: Find the differential equation of the following function (x – 3y + 2)dx + 3(x+ 3y – 4)dy = 0 x-1 a.…

A: The given differential equation is x-3y+2dx+3x+3y-4dy=0.....(1) We shall solve the differential…

Q: 1. Solve for x(t) and y(t), given that x(0)=D4 and y(0)=3 dx dy + x + 4y = 10; a dt dt x(t) 2+2e cos…

A: Solution :-

Q: Find the differential equation of the following function (х — Зу + 2)dx + 3(х + Зу— 4)dy %3D0 х-1 а.…

A: Let us consider the differential equation of the form dydx=ax+by+cdx+ey+f To solve the equation…

Q: 7. When the given differential equation is Solved using Laplace transform Method, the equivalint…

A: Given  differential equation isy''+2y'+y=te-tand given conditions are y0=1 and y'0=-2find the…

Q: 19. Solve the following differential equa- tions using classical methods. Assume zero initial…

A:

Q: 13. Find the differential dy for each of the following. a) y = cos 2x- sin 3x b) y = x2 – V36 – x² |…

A:

Q: 7. Solve the following Cauchy-Euler equation d’y dx² dy +5x- +3y = In x. dx

A:

Q: 4. Show that :| f(t) sin a(x – t)dt Y : solves the initial value problem dy +a²y = f(x), dx? dy 0…

A: Below is the answer

Q: Solve the following initial-value problem: /3 V1-y? dx - V1 - x² dy=0; y(0) = O sin-x- 2sin-ly=…

A:

Q: Q3.B. Find a general solution of the following y" - 4y' + 4y = 3sin(2t) differential equation using…

A:

Q: The solution of the following exact initial value problem (y cos x – xy sin x)dx + (x cos x – 1)dy =…

A: does not satisfy

Q: 1. [8te" dt 2. . (1–3x)sin(}x)dx 3. w'e*™ dw 1-1

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

Q: Solve the following initial-value problem: V3 V1-y? dx - V1- x² dy=D0; y(0) = 2 O 2sin-1x+sin-ly=t/3…

A: Given: The differential equation 1-y2dx-1-x2dy=0 and initial condition y0=32, To Find: Solution of…

Q: 1. -ay + A sin dy 2 = Br, dt

A:

Q: 2) Consider dx dy_ 2x+1 Зу? a) Draw a slope field to the left. b) On the slope field, sketch the…

A: The given differential equation is: dydx=2x+13y2

Q: 1. Solve the initial-boundary value problem du 2 32u 0 0 %3D 3 dx? u(0, t) = u (4, t) = 0 t >0 3Tx…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Find the solution of the given initial value problem in explicit form. 75 π sin (2x) dx + cos (7y)…

A: The given initial value problem is                        sin2xdx+cos7ydy=0,  yπ2=π7 We have to find…

Q: 1) Solve the following Partial Differential Equation: Ut + (2x – t)Ux = x , with U(x,0) = sin(x)

A:

Q: 1. Solve the initial-boundary value problem du 2 32u 0 0 3 dx2 u(0, t) = u (4, t) = 0 t > 0 u(г,0)…

A:

Q: Proceed as in this example and find an explicit solution of the given initial-value problem. dy = y²…

A:

Q: SOLVE the following DIFFERENTIAL EQUATIONS * for partial derivative symbol, use the letter d 05…

A: To solve the differential equation.

Q: 4. a) Transform the following Cauchy Euler equationto a differential with constant coefficients by…

A:

Q: 1. Solve the initial-boundary value problem ди 2 02u 0 0 3 dx2 u(0, t) = u (4, t) = 0 t20 3Tx u(x,…

A: As per guideline solving only 1 question

Q: Find the general solution of the nonhomogeneous equation y " - 3 y "+4 y ' – 12y =e + 2 1 3* + C,…

A:

Q: Determine the solution of an initial value problem; 2e'cos2r dx + (e'sin2r+3y sec?y²) dy=0_y 0= (A…

A:

Q: Find an explicit solution of the given initial-value problem. √₁ - y² dx - √1 - x² dy = 0, y(0) =…

A:

Q: 4. Find the explicit particular solution of the initial value problem give dy -уе , у(0) %3D 9 е 8x…

A: We will find the solution to the Differential equation.