(6) The Non-homogeneous Heat equation 4 t = 4uxx + x3 0 0 1 u(0,t) = 2 " Ux (2,t) = 0 u(x,0) = x² under the assumption u(x,t)=w(x,t)+v(x), then v(x)= -x5 (a) -+x-2 (b) 80 -x5 -x5 80 +x+1 (d) - 80 ד ר7 -+x+2 (c)- 80 +x-1 (e) None of these

Q: Find exactly T(t) and N(t) for x = e'cost, y = e'sint, z = e' for t = 0. [Choose the correct…

A: This is a problem of Differential Geometry.

Q: The general solution of the equation: t?y" + 2ty' = 0 is y = c1+ c2/t. You use the variation of…

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Q: Find the general solution of dy + y cot(x) = 6 csc'(x). dx

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Q: 2) Let y = c,x + C,x ln x be the general solution to x'y" – xy' + y = 0 on(-∞,). Find c, and c, such…

A: Given that the below equation is a general solution of x2y''−xy'+y=0. y=c1x+c2xlnx To find the value…

Q: 6. A mass-spring-damper system has the equation ma" + ßx' + kx = F(t), where r(t) is th displacement…

A: Given , mass-spring-damper system equation as- mx''+βx'+kx=Ft To find the units of β and k in the…

Q: xyz" + (y +z)' + x'yz z(xy' + z)(x + y')

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Q: Find all equilibrium points of X' = x(0.3 – 0.01y) y = y(15 – y+25x)

A: Given  x'=x0.3-0.01yy'=y15-y+25x

Q: Let y1, Y2 be two independent solutions of (t – 1)y" – ty' +y = 0. If W(y1, Y2)(2) = e² , then W…

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Q: Consider the nonhomogeneous linear equation y" +9y' g(t) with the complementary solution y,= c1y1(t)…

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Q: Obtain two linearly independent solutions valid near x = 0  xy" + x(x - 1)y' + (1 - x)y = 0

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Q: 3. Use your solution from Part 2 to give solutions to the IVPS i. y" + 2y' + 16y = cos 3t, y(0) =…

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Q: Determine the homogeneous solution of the ODE y" - 8y" + y' + 42y = 2e^3x + 1 a. C1*e^(-2x) +…

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Q: Let y= ao+ a1t+ azt + a3t³ + azt“ + ast° + agt°. d'y +...... be the solution of dy + t- dt ; y(0) =…

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Q: Let y be the solution of y'+y=x, xER,y(-1)=0. Then, y(1) 류를 ²-28² 2-2e -

A: Since given that y be a solution of differential equation…

Q: Find exactly T(t) and N(t) for x = e'cost, y = e'sint, z = e' for t = 0. [Choose the correct…

A:

Q: Let y1, Y2 be two independent solutions of t?y" – 2y' + (t + 3)y = 0. %3D If w(y1, y2)(2) = 3, then…

A:

Q: (i) Consider the LU factorization 0 0 [b, C1 a2 b2 C2 0 0 a3 bz C3 as b, 14 0 0 01[1 u 0 0 01 U2 0 1…

A: Given:  To show: , , ,

Q: 2. Use separation of variables to solve (a) y' = -2y, y(0) = 1 (b) 4y' = y², y(0) = 4 %3D (c) y' + y…

A: Note:  "As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: Write the system x'= e"x – 4ty+9 sin(t), y' = 7 tan(t)y + 9x – 4 cos(t) in the form = P(t) + F(t).…

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Q: c'(x) = e(x) e'(x) = t(x) t'(x) = h(x) h'(x) = c(x) 0 1 2 1 0 4 3 3 4 1 2 لا e(x) c(x) 3 t(x) 4 1 3…

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Q: Consider the following. x' = 4x + y y' = −2x + 2y,   X(0) = (−1, 2) The general solution is (x(t),…

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Q: Let y(t) be the solution to y˙=5te^(-y)˙ satisfying y(0)=−3  (a) Use Euler's Method with time step…

A: Euler's method is a technique for numerical differentiation in which we compute the approximation of…

Q: Illustrate the numerical approximation of solutions of systems x' = f (t , x) ,    x(t0) =x0

A: We have to give an approximation method to solve given first order differential equation .

Q: Find all functions that form a fundamental set of solutions for t2y" – 2ty' + 2y = 0. O y(t) = et O…

A: We have to solve given problem:

Q: (d) Find all possible values of a, b, c so that U(x, t) = ax² + bt + ct² solves the heat equation…

A: To find the values of constants, we need to plug the given function into the differential equation.

Q: Q3) Solve the heat equation u=u u t ¸ (0,1) = u(x,t) =0, t>0, u(x, 0) = 1, 00 with

A: Step 1:Step 2:Step 3:Step 4:

Q: Obtain two linearly independent solutions valid near x = 0  x(1 - x)y" - 3y' + 2y = 0

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Q: 17. Evaluate L{y"(1) + 2y'(1) + y(1)}; y'(0) = -1, y(0) = 5. Let L {y()} = {s). A) (s°+2s+ 1)Y(s) –…

A: Here we use basic laplace transform

Q: Find a particular solution to y"+ 2y'+ y = 1 (A) (B) y, = 21-1 %3D (C) y,-2r-2 Y, = (D) y, =1 (E)…

A: