Select an area to comment on 5. Solve 0 < x < 1,t > 0, 0, u(1,t) = 0, t>0, 0 < x < 1. Uxx – 4ug Ut, u(0, t) 2x u(x,0)

Q: y" + 3y' +2y=(− 4x² − x + 1)cos 2x − (2x² + 2x +1)sin 2x

A: To solve the differential equation of the form y''+ay'+by=A(x)cosbx+B(x)sinbx Assume the particular…

Q: (x*D}-2xy0,D, +yo;-xD,+3yD,)z=0

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Q: (1+x²) uz + Uy = 0, u(1, y) = sec y

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Q: ) Write the solution of each initial value problems as integral equation, integrate if possible and…

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Q: r -t = sin 2x cos 3y + (x + y).

A: In this question, we solve the non-homogeneous partial differential equation by the operator method.

Q: Classify the following partial differential equation according to the sign of the expression B²-4AC…

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Q: 8. Obtain the general solution to the equation ( Dª - 3D³ + 5D² - 9D + 6 )y = 0 a. y = cie* + c2e2x…

A: If the roots m1,m2,...,mn of the Auxiliary equations are distinct and real then the complete…

Q: Consider the 1 -Au = Au = 1 x² + y² ≤ 1, u(x, y) = 0 x² + y² = 1 1 Find u (0,0). Hint: You have seen…

A: As per the question we are given the following boundary value problem : (-1/4)∆u = 1  for  x2 + y2 ≤…

Q: Find a solution to the boundary-value problem y" + 4y = 0; y () = 0, y () = 1, if the general…

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Q: on of y' =x+x 1 +.

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Q: Q.2 Consider the function f(x) =- J1-x², 0<x<1 Find and x-1, 1<x< 2 sketch the odd and even…

A: Given function is fx=1-x20&lt;x&lt;1-11≤x≤2 To find the extension of fx in [-2,2]. That is to find…

Q: Solve the system of differential equations (x₁=214x1+90x2 ₂-504x1-212x2 *1(0)=-1, x₂(0) = 2 x₁(t)=…

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Q: dx/dt+dy/dt+x=e-t dx/dt+dy/dt-x-y=e2t     x(t) general function solutions

A: This system has been solved by the elimination method, by eliminating y to get the general solution…

Q: azu(x, t) a?u(x, t) (-00 0) at2 ax2 u(x,0) = 4e-5|x| %3D (x,0)30 at

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Q: Solve y" (t) + 2y' (t) + 2y (t) = H (t); y (0) = 1 ; y' (0) = 0 where H(t) = 2t + 3,0 < t < 1 H(t) =…

A: *This problem is too lengthy.That's why I have used partial decomposition calculator to find partial…

Q: 4x y"+8xy'+ y=0 solution of the given differantial equation is y = C,x" +C,x" In x → n = ? O A) -3/2…

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Q: 7. Find the general solution of ( D5 + 3D4 – 21D³ – 47D² + 120D + 144 )y = 0 a. y = ciex + c2e3x +…

A: To find out the general solution.

Q: Consider a slightly damped vibrating string that satisfies du 8²u 8² u To po at² = B- მ2 Ət (a)…

A: Given: The equation is  ρ0∂2u∂t2=T0∂2u∂x2-β∂u∂t. To find: a) Reason of β&gt;0.             b)…

Q: ду if cosh(3x?y) %3D х + In(e*У + 1) ax

A: Given that cosh3x2y=x+lnexy+1                            ……(1) We have to find ∂y∂x Partial…

Q: Differential Equations

A: Step 1:Step 2: Step 3: Step 4:

Q: a)-7y=sen (2x) dx

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 3. Find the general solution of the partial differential equation *** (x" + y" )z ; m, ne IR* . ây

A: Find the general solution of the partial differential equation: xm∂z∂x+yn∂z∂y=x+yn+mxm+ynz ,  m,n∈ℝ+

Q: Ow ôw – 2xy 4. The partial differential equation +w |=0 _is classified as +

A: The solution are next step

Q: 2. ORDINARY DIFFERENTIAL EQUATIONS " Solve the integral equation, y(z) = 2 + y(t) 3. LINEAR ALGEBRA…

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Q: (d) Lu=ux + Uy + 1

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Q: y"+ y' =2 y = x² +e* the particular(nonhomogenous) solution of the given ode is y, = * ax +bx+ c +De…

A: We don't need to find whole yp, since our requirement is only the value of D

Q: y"" − 3y" + 2y' = www. @2x 1+e*

A: Given that y'''-3y''+2y'=e2x1+ex

Q: if we use u=y substitution for the following bernouilli equation 1 y'+ 2х -y = xy* we obtain, u'+…

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Q: 22u 2t2 = 4 22u 0х2 u(0,t) = u(п,t) = 0 = u(x, 0) = 2 sin(x) + 5 sin(3x) + sin(5x) ди (x,0) = sin(x)…

A: The given problem is to find the solution for the given partial differential equation with given…

Q: azu(x,t) azu(x, t) 9- ax2 (-00 0) %3D at2 u(x,0) = 4e-5x| %3D

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Q: 2 By = 2x3 + 3xy + 10 when y = 0, Ju ду = sinx + 3 and u = 0

A: We have, a second order partial differential equation . We need to find the value of u here. Here,…

Q: sketch the odd and even extensions for -3,3]. Use the substitutions : '= ye¯* s = x Q.3 to solve the…

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Q: ei y trêu giả =0 x,y>0 Write down the characteristic equation and solve it. draw the characteristic…

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Q: Find the general solutions of the equations i) u -4u, +u, + 2u, = 9 sin(3x- y)+19cos(3x – y) %3D

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

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.