Let u(r, t) denote the solution of the following initial-boundary value problem du 0SIS1, t>0 20t uz(0, t) uz(1, t) = 0 %3D u(x,0)

Q: 1-find both first partial derivatives  f(x,y)=x^2 e^xy

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

Q: (1,2) 6. Evaluate 0,1 (x²-y) dx + (y² +x) dy along a straight line from (0,1) to (1,1) and then from…

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Q: 2. Find the general solution of x*v + 1) dx + y'(x - 1) dy = 0 x2 - y? + 2x - 2y + А. 2ln[(y + 1)/(x…

A: No option is matching the final answer. All the given four options are incorrect. The correct answer…

Q: yd the geroral solution uf y3y'+2y= 4&=2xe

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Q: Show that the solution of the equation dx/dt=-x(k^2+x^2) With initial condition…

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Q: 6. A particle is travelling along the circular path x² + y² = 100. At the moment when the particle…

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Q: Find an equation of the tangent line to f (x) = x² Vx4 – 12 at x = 2. - %3D

A: Explained below

Q: Solve the IVP y" + 2y' + y = U (t – 3), y(0) = 0, y'(0) = 1. -

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Q: Find a particular solution of the equation y2y' = cosx satisfying the initial condition y(0) = 0.…

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Q: Construct a finite difference method to approximate the elliptic partial difference equation Uxx +…

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Q: Q1 (C) Let a and k be constants. By implementing partial derivatives, prove that the function u…

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Q: 2. Explain why the system f x' {y'. 9 1 + f² + g² 1 + f² + g² trajectories as x' = f(x, y). y' =…

A: The given system of differential equations is: x'=f1+f2+g2y'=g1+f2+g2 The objective of the question…

Q: Differentiate x + y = e2x+2y A. 1 – 2e2x+2y 1+ 2e2x+2y y' В. -1 + 2e²x+2y 1 – 2e2x+2y y' | С. ||

A: Given query is to find the derivative of the expression.

Q: If L(x, y, y/) = y² (1+ (y/)²)³ what are Ly and Ly? O Ly = 2y(1+ (y)²)³ and Ly = 6y"y² (1+ (y')²)² O…

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Q: Find the first partial derivatives of f(x,y) = 5 ex°y of 30 e %3D

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Q: determine the nature of the critical point and draw the phase plane of x'=Ax d) e) (-2-3) 3-4 1 -1

A: The System of Linear differential equation x'=Ax has only (0,0) critical point .  (i) If the both…

Q: x(0) = -2 y(0) = 2 x' = -2x +y y' = -5x + 4y (x(t)) diferansiyel denklem sisteminin çözüm vektörü…

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Q: x²dy + (y² + 3xy + 4x²) dx = 0 when x = 2, y = 1

A: To obtain general and particular solution satisfying initial condition indicated byusing homogenous…

Q: variation of parameter

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Q: Solve the 2 dy JX Y(1)=1 S Following initial value problem x²=2x² x(y +1)+(y+1) X T

A: The initial value problem is x2dydx=x3-2x2xy+1+y+1 with y1=1. The objective is to solve for yx. The…

Q: What is the solution of given initial value problem? =y + sin t dt2 da + cost dt - dt2 * (0) = 1, a…

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Q: Solve the 2 dy JX Following initial value proble x-2x 4 + T XI 4

A: We have to solve the given initial value problem.

Q: solve  utt- 4uxx=x2          -infinity 0  subject to initial conditions: u(x,0) = x  ut(x,0)=0

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Q: 4. J(2y + 3)? у+2 dy

A: Find your answer below

Q: 2. y' y' = y+x²y , y(0) = −2

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Q: Obtain general solution of the D.E. y + (1/3)y = e'y A) 1/x = e (c - 3x) B 1/y³ = e* (c - 3x) 1/y =…

A: The given equation is Bernoulli equation we will solve this by substitution method

Q: Let y= ao+ a,t+ azt² + azt³ + a4t“ + agt + ag d?y +6 be the solution of .... .. dy +t +y=tan-'t ;…

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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.