Solve du a²u k xe (0, L), t>0 ôu (0.1)- ĉu (L,t) = 0 ди (0,1): Əx 87x - 3 сos L 3n x u(x,0) = 10+5cos L

Q: 4. If integration using u-substitution technique is used to solve for correct choice for u? (a) u =…

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Q: at Solve thie équation use Eulers methoc- ds -t X-ツ dx x+y y(6)%=1

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Q: . (solve exact de) (2ysinxcosx - y + 2y?e*v* )dx = (x - sin?x - 4xye*)dy

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Q: dz b- Solve by chain rule to determine dx z = x²y* -2y , y = sin(x²)

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Q: Find the particular solution of y (9x - 2y) dx -x (6x - y) dy=0., when x=1, y=1. Let x=vy

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Q: Solve simultaneous equation dx/dt=x+y , dy/dt=4x+y , t=0 , x=2 , y=5

A: First I have written the differential equation into operator form and then reduce it into linear…

Q: Solve the homogeneous DE 3xy dx + (x^2 + y^2) dy = 0.

A: We will take the substitution y=vx, to convert it into separable variable form.

Q: y" + y = sec x tan x

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Q: 1) = sinx + ytanx dy dx 2) x = y + x sin? 3) Prove that (2xy – 9x2)dx + (2y + x² + 1)dy = 0 is…

A: 1   dydx=sinx+ytanx        the equation can be written as standard form        dydx-ytanx=sinx…

Q: dx dt -x + y + 2et ip dt — у — е-t

A: System of differential equation

Q: Show that if you differentiate both sides of x2 +2y³ = 6, the result is dy dx 2x + 6y² = 0. Then…

A: Given function is x2+2y3=6 Power rule of differentiation states that  ddxxn=nxn-1 And ddxconstant=0…

Q: 1. 3(3x2 + y²)dx – 2xydy = 0

A: According to our guidelines we can solve only the first question. Please re post the other questions…

Q: b) Solve by using Runge-Kutta method to find y,. dy = x + cos(y) ; 0Sx<1 ;y(0) = 1; h = 0.5 dx

A: Solve the intial value problem, using Rung-Kutta method

Q: x°y" + 2x?y"+ xy'-y=0

A: A homogenous linear differential equation with variable coefficients given by,…

Q: obtain the particular solutions satisfying the indicated conditions: dx/y=(25-x^2)^-1/2dy; y(0)=1

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Q: Use the differential dy to approximate Ay when x changes from x = -3 tox = -2.99. y = x2 + 1 Enter…

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Q: I-x² f (x, y, 2) dz dy dx 1-x² Jo

A: we have to find the region of integration

Q: (2y-x)(dy/dx) = 2x + y, given that y = 3 and  when x = 2 Homogeneous equations

A: Solve the following problem by substitution.

Q: 1. Obtain the General Solution. Use reduction to exact. Simplify your fin y(y + 2x- 2) dx - 2(x +…

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Q: we solve thd DE y dx 2x0y-0aer convedding it to oad sing an integrating tactor, then the solution…

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Q: w = In(x²+y² +z²) x = cost y = sint z = 4E

A: w=lnx2+y2+z2, where x=cost, y=sint, and z=4t. Find dwdt.

Q: Use Picard's method of successive approximation to solve the equation 1+ xy, y(0) - 1 at x-0.1.

A: The solution of the differential equation is defined as the function that satisfies the equation.…

Q: To integrate x3x² dx' Ox хех2 242 x² OX we apply integration by parts and in the form u dv, dv is…

A: We have to determine the integral

Q: Use Variation of Parameters to find a particular solution to the non-homogeneous equation y′′−2y′+y=…

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Q: I the function z(x, y) = ex sin(3y) and x = ut-t², y = √u² + t², Find : dz dz and 2- (by chain rule)…

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Q: Obtain the solution using Integrating Factors Found by Formulas. 2(2y2 + 5xy- 2y + 4)dx + x(2x +…

A: We can solve this using integrating factor

Q: (b) Given that y, = z sin(ln z) solves r*y" – xy + 2y = 0, %3D

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Q: Test for exactness and determine the particular solution of: (yexy – 2y³)dx+ (xexy – 6xy2 – 2y)dy =…

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

Q: 2(y-4x2) dx + x dy

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Q: xy' + y = sin(x), y(3) = 0, y'(3) = 0. Yh = C1x + c2x ln(x).

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Q: Solve the disfertial equation xy' -Y =Xtan ) %3D

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Q: Solve ởy ôt y (x, 0)= 3 sin 2n x, y (0, t) = 0 = y (1, t); 0 0. %3D ốt

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Q: Eliminate the arbritrary constant/s. Show full solution. x= -In t, y= at + bt?

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Q: II. Solve th following DEs by LT. 1. y" + 2y' – 3y = sin(2x), y(0) = y'(0) = 0 %3D -

A: We are given a linear second order nonhomogeneous differential equation with constant coefficients…

Q: (3x + 2y3) dx + 3xy2 dy = 0 ,  y(1) = 1

A: Given: (3x + 2y3) dx + 3xy2 dy = 0 ,  y(1) = 1

Q: Use Euler's method to estimate y(0.02) ey-x y' = 1+e3y „y(0) = 4 0.01) What is the error in the…

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Q: Find the particular solution of y(9x-2y)dx - x(6x-y)dy= 0, when x=1, y=1. To start, let y=vx.

A: The given differential equation isyax-2ydx-x6y-ydy=0, with y1=1It can be written…

Q: Find the solution of the differential equatlor dy 3xeY, y(0) = 0 dx %3D

A: Consider the equation

Q: B. In each exercise, obtain the particular of solution. (y+ Vx² + y²) dx – x dy = 0; when x = /3, y…

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Q: 2. u(x)= secx+à So u(1)dt.

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Q: Solve the Euler equation d²y dx dy -5y = 0 dx 31 d', 3x2 given that y(1) =1 and y'(1) = 2. intai

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Q: Obtain the solution using Integrating Factors Found by Formulas. 1. 2(2y2 + 5xy – 2y + 4)dx + x(2x +…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Solve the differential eavations ydx xdy = 0 x' +y° +y?

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Q: •ý -2ý +y= ě sinx %3D Ans: y=ě +2xě - ě sinx • ý -uý ruy = 12 /* %3D e 2X 2 ZX .2 +C2 X e + 20

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: Solve for x = u + 1 and y = 2u² - 4u d²y dx² with respect to the parameter u

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Q: Obtain the solution using Integrating Factors Found by Formulas 1. 2(2y2 + 5xy – 2y + 4)dx + x(2x +…

A: A detailed solution is given below.   (As per our guidelines, we have to solve only 1st question)

Q: Obtain the general solution using separation of variables dx = t(1 + t²)sec²x dt

A: Given: The differential equation dx=t1+t2sec2x dt . The given differential equation can be…