EXAMPLE 3: Solve the differential equation y" + y' = 3sin(2.x)+cos(2.x).

Q: If 7'(t) = (cos t, e²“, 3t²) and 7(0) = (3, 1, –2), find the function 7'(t).

A:

Q: Đạo hàm riêng cấp hai của hàm f(2, 3) =ln(22+3y) theo biến y là fyy (2, 3) theo bien y, xlà f, (x,…

A:

Q: h (y) — Зу 6 — 8у 3 + 9у 1 -9- |

A:

Q: af find given f (x, y) = e + 2xy² - 4y at (0,3) 9 ду O-12 O-7 O 8 O 4

A:

Q: From your sketch, what is the equation of the solution to the differential equation that passes…

A: The complete solutions are given below

Q: Let'W (s, t)= F(u(s, t), v(s, t)) where W,(1,0) 6 We(1,0) = u(1,0) = -7, u,(1,0) = -6, u,(1,0) = -5…

A:

Q: Functional theory and functional analysis

A: According to the given information it is required to prove that:

Q: let a=(2,4-3), 6=(60,1),c=(0,-1,5) eguation of line thoough ' parallel to % what é the @) Yhe 6) Khe…

A:

Q: These exercises involve functions of three variables. Let f(r, y, 2) = xy²z' + 3. Find (a) f(2, 1,…

A: Function in three variable are given, we have to find the required values

Q: da m- dt? +4. + 6x | dt is overdamped, the range of values for m is? | Your answer will be an…

A:

Q: f(x, y), x = x(u, v), y = y(u, v), with x(2,5) = 1 and y(2,5) = 4, calculate Z₂ (2,5) in terms of…

A:

Q: Linear Alegrba and Differential Equations

A:

Q: If y(x) = uv, then y' is *

A: This is an example of Product Rule of Differentiation

Q: 2x+3xz-wx Let f (x, z, w) x+z Find: a(x,z,w) blank 1: evaluated at x=z=w=1 a(x,z,w) blank 2:…

A:

Q: Let a function f(x, y, z) be such that Vf(P)-[4, 3, 2] The value of directional derivative D,f(P)…

A:

Q: Are the functions ³ y₁(t) = 1−³, y₂(t) = = t a fundamental set of solutions of t²y + 2ty -6y=0

A:

Q: Consider the data given below: -50 -25 25 50 75 100 125 (x) 43+NI -20 round(N2/10) 32 5+NI/S 67 79…

A: Consider the data given below: x -50 -25 0 25 50 75 100 125 fx -38 -20 5 32 6 67 79 83 The…

Q: (i) If y =g (x1- x2). Let u = x1- x2, show that (a) ay/du = ây/Əxı=- dy/ax2 %3D (b) a@y/ðu² = y/Əx¡²…

A:

Q: I y - (x-2)² y-y (y- y)² 2 (x - x) (y - y) 0 3 -2.33 5.43 1 1 -2.33 4 2 1.67 2.79 0 0 0 3 0.67 0.45…

A: Step 1:Calculate the slope and  the y-intercept of the regression linePart a;m=Sxx​sxy​​part…

Q: 日-[ 2 2. (5pts) Let vị = Find all values of x so that the set {v1, V2} is -3 - V2 = linearly…

A:

Q: Let f(x, y, z)=xze +3(x+y)-xz³. Then the derivative off in the direction of v=7+j+2k at the point…

A:

Q: | f(t) dt 20z 4, then f (t) dt is If 4x²+21

A:

Q: x 1 2 3 F(x) 5 10 25 F`(X) 2 3 5 find the approximate value of F(2.1)

A: f is approximated as,

Q: BCShow that the nonlinear ODE y'(t) = (a + by)(c(t) + d(t)y), where constants a, b + 0 and c(t),…

A: Substitute y=bz-ab............(1) Now differentiate the above dydt=b-1z2dzdt           ........(2)…