ди If u(x, y) be the solution of given partial differential equation = 4 ax du given that u(x,0) = 8e-12x then which of the following is the value of u(x,y)? %3D (a)8e-12r-3y (b) e-12x+3y (c) e12x+3y (d)-8e-12r-3y O a Oc

Q: 2] The linear differential equation with constant coefficients satisfied by the equation y = 2x 5e2*…

A: Hence option (b) is correct.

Q: 23. For the differential equation y"+y = 3 sin(2t) +t cos(2t) the form of the particular solution is…

A:

Q: Find the solution of the differential equation у" — 16у 3D 2е\x y = C,eªx C2e¬4x + +xe4x а. 4 b. y =…

A: The given differential equation is y''-16y=2e4x .............................. (1)  for the…

Q: The general solution of the homogeneous differential equation 3x y" + 7xy + y = 0 can be written as…

A:

Q: The differential equation y" + 4y + 4y 0 has two solutions yı = e2x and y2 = Which of the followings…

A:

Q: The second-order linear differential equation xy" + 2y' 12x can be solved by first making the…

A:

Q: (5) The partial differential equation corresponding to u= = f(x? + y°) is у ди ди (a) x ôx ди (d)…

A:

Q: What is the general solution to the differential equation 2(x – y²)dx + x(4y + x)dy = 0 ? у3 — ху? +…

A: The given differential equation is of the form of Mdx+Ndy=0.First we check given differential…

Q: Determine which of the following are ordinary differential equations and which are partial…

A:

Q: mh" +5h' +120h = mg h(0)=100 h'(o)=0

A:

Q: The solution of the non-exact differential equation 2ydx + (3y-2x)dy = 0 is (2x/y)+3lny=Dc O…

A: Given  2ydx + (3y - 2x)dy = 0

Q: Evaluate the porticalar çoution of: y(み-yty)x - x(4-y)dy %=o when x=1, y = 2 A- y?Inx + xy + x* =…

A: y(2x2+y2-xy)dx - x2(2x-y)dy = 0 dydx=y(2x2+y2-xy)x2(2x-y) dydx = (2x-y)xy + y3x2(2x-y) dydx = xyx2 +…

Q: The differential equation y' = Vx+y+1–1 has the solution:

A: We need to solve the differential equation given by y'=x+y+1-1 The solution is given below.

Q: The differential equation, (x + 3y - 5) dx - (3x + y - 7) dy = 0 can be transformed into homogeneous…

A:

Q: The general solution to the differential equation - 2 ()- is dr = 0 is | dt3 dt2 dt O x = C1 + C2e +…

A:

Q: Given that ₁ A₁ = 6 = H -A help (numbers) and 72 = are eigenvectors of the matrix A₂ = 2 help…

A:

Q: ди ди +x (e) Solve the partial differential equation: 2y- Əx ду = -2xyu, where u = u(x, y)

A:

Q: azu Solve the partial differential equation du = 1 ax sin(x + y) given that at y = 0, and %3D дх ду…

A: The given partial differential equation is,∂2u∂x∂y=sinx+yGiven that, y=0, ∂u∂x=1 and x=0, u=y-12To…

Q: What is the differential equation of the solution y = C1e®" + C2xe®u + C3e¬7w ? O y" – 11y" + 45y +…

A:

Q: The transversality condition holds for the partial differential equation X4x +Uy=0 with the initial…

A: In the given question we have to check the transversality  condition of the given P.D.E s.t xux+uy=0…

Q: Determine the solution of the differential equation + 12 + 8 = 0 ds ds ds ds x = C, + C2s + Czež +…

A:

Q: Find a basis for the subspace of R³ spanned by S. S= {(4,2,-1), (1,2,8), (0,1,2)}

A:

Q: DEGREE

A: We have to determine the order, degree and linearity of the given differential equations according…

Q: The statement "If u, and u₂ are any solutions of a partial differential equation then so is cau, +…

A: Solution:

Q: (D? + 3D + 2)y = 12x2 A. y = ce* + cze-2x B. y = ce* + cze-2x + 12x² C. y = Ce* + Cze 2* + 6x² – 18x…

A: A detailed solution is given below

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.