11. Find the solution of the initial value problem u" +u = F(t), u(0) = 0, u'(0) = 0, where F(t) = Fot, Fo(2π-t), 0, 0≤t≤π, π < t ≤ 2π, 2π

Q: x²y" − x(x + 2)y' + (x + 2)y = 0, 0 < x

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Q: (x^2)y''-2xy'+2y=0; y(1)=4, y'(1)=7   Find particular solution that satisfies the given condition

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Q: If U and V are positive constants, find all critical points of F(t) = Ue' + Vet.

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Q: 3(3y² + x²)dy - 2xydx = 0 when x = 3, y = -2

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Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

Q: Let A 22 = - (²3) 11 Find the solution of the problem: X Y = AY + [*]. Y = (0) -X

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Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+ C₁e-ax using…

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Q: 5. Find a particular solution to the equation -2x y" + 4y' + 4y = xe¯

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Q: Find y' if ey+y²=2x. yey – 2 y'= хе + 2у хе + 2у y'= ye – 2 хе*У + 2у y'= 2 – yey 2 – ye y'= хе*У +…

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Q: f(x)= k(3x + 4), x = – 1,0,1,2 Find second moment E(X').

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Q: Solve u' (t) + u(t) = 5 subject to u (2) = -2. 85 Provide an exact expression (i.e. no decimal…

A: Question - solve u'(t) + u(t) = 5 subject to u(2)=-2

Q: Consider the following initial value problem 3 3 6y" + 6y(x′)³ +48 (v′) ³ = 0, 3(0) = −5, 3/(0) = 27…

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Q: What is the solution of the given ODE xy' + y = Vx

A: Given: xy'+y=x

Q: (2) Solve the following PDE for u(x, y): a'u 1- +30u 18x-3x +2

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Q: y" – 2y' + y = –3 – x + x²,

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Q: Find general solution of U" + U = 0.

A: Given differentiation equation is U''+U=0. We have to find the general solution of the given…

Q: Solve the inital value problem 2xy'+y=6x  for x is greater than 0 y(4)=26

A: Given:           2xy'+y=6x ;   x&gt;0,  y(4)=26

Q: Solve Ut = Urx, x > 0, t> 0, u (x, 0) = f (x), u (0, t) = 0.

A: Given partial differential equation isut=uxx,     x&gt;0,     t&gt;0ux, 0=fxu0, t=0

Q: Suppose that x-y" + axy' + by = 0 has the general solution of the following form: y = C,x³ + C2x³ In…

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Q: Which of the following is a solution to x' A(f) x +b (t) if -2 1 A (1) = -3 2 b(t)= 2 sin(t) -…

A: To find -

Q: xy' + 2y = 3x, y(1) = 5 %3D

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Q: 4. a) Find the general solutions of the following differential equations. Express the general…

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Q: 2) Find a general solution to the following Cauchy-Euler equation for t > 0. (t^2)y"+3ty'+10y=0

A: Given: Here, the given details are, The given equation is, t2y''+3ty'+10y=0. To find a general…

Q: Find the general solution of the inhomogeneous second-order linear ODE 2( 24" - 5' 3u)= 2(10 sinx)

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Q: 5. Use variation of parameters method to solve а. a. y" – 2y' + y = 1+x2

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Q: Find solution of IVP y" - 4y - 5y = 0 y(1) = 8, y'(1) = -5.

A: Given the differential equation is                        y''-4y'-5y=0, y(1)=8, y'(1)=-5.