Solve the heat equation by using the method of separation of variables u, - ku = 0, subject to boundary conditions 0< x< L, t> 0 u, (x,0) = u, (x, L) = 0 and initial condition 9nx u(x, 0) = 9 sin( where k is a constant.

Q: y" +y = 3 et/2) y(0) = 4 y(0) = 3

A: Second order non Homogeneous differential equation

Q: FIND 2 DIFFERENT (LINEARLY IN DE PENDËNT ) SOLUTION S POR THE D.E y"_x² y'- 3 xy = O *y'-3xy%3D0

A: Step:-1 Given that y''-x2y'-3xy=0 ---(1) This is second order differential equation with variable…

Q: 2²y" - 4.xy+6y= 0, y(2)=0, y'(2) = 4 %3D

A: The differential equation is given as x2y''-4xy'+6y=0x2D2y-4xDy+6y=0x2D2-4xD+6y=0 It is a Cauchy…

Q: Use the annihilator operator (not undetermined coefficient) for the right hand side and use it with…

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Q: Choose the solution value of x'' + w2x = fsinwt with initial conditions x(0) = 0 and x'(0) = 0

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

A:

Q: Find the solution of the IVP x" - x' + 5x = 4+ u₂(t)e-2(t-2) x(0) = 2, x'(0) = -1 where u₂(t) is…

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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: the non-homogeneous equation y” – 2y’ = t + e^t, then determine this solution

A: Given non-homogeneous differential equation We have to find the solution of the differential…

Q: 1. y' = 2x x y. 4 x {y=4+ 6x3 C-X 3

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Q: Verify that y = 1/(x+ C) is a solution to y'= -y², where C is some constant. Find the particular…

A: Given that: y=1(x+C)

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.