| (t+8)(t+3)dt.

Q: 9. Solve d²x dt² + 4x + 5y = 1²; d²y dt² + 5x + 4y = t +1.

A:

Q: (b) ruz – 2yuy + u = eª , for x> 0

A: 1.(b) Given partial differential equation xux-2yuy+u=ex, for x>0 This can be written as…

Q: Find the general solution of each ff Higher-order DE using Reduction of Order  1. (2D2 + 3D -2)y=0

A:

Q: Find high order DE 6. (D4-5D² - 36)y = 0

A:

Q: d²y dy – 4 + 4y = e2t.t dt2 dt

A: our objective is to solve the differential equation

Q: 3. 2t t dt ST-t

A: To integrate the given vector function. ∫te2t, t1-t,11-t2dt...(1)

Q: 5T 1 y=-2cos(Gx+っ)+1

A: Phase shift: -5π

Q: (c) Show that V(3) = o²(X'V-¹X)-¹.

A: 3. c From the given information, y=Xβ+ε Eε=0, Vε=σ2V From the part b, β^=X'V-1X-1X'V-1y

Q: 1 | t(t + 3) dt -1

A:

Q: In(ax) f(x) has a stationary point at Find a and b. bx 2' 3e,

A:

Q: wouldn't there be a t in the second term of the general solution?

A:

Q: 2 3 dt. 0 1+t2

A:

Q: (2) = [ (t² − 1) dt (b) f(x) =

A:

Q: The Power Chain Rule simplifies computing the derivative of a powerof an expression

A: To find the derivative of a power of an expression using the chain rule. ddxe3x+1 Solution: Chain…

Q: 2t + 3 r(t) -, In(t² + 2) t2 +1

A:

Q: 2. x"(t) – 4x'(t) + 4x(t) = 4e²t; x(0) = –1, x'(0) = -4 %3D

A:

Q: 2 c4 e-x-2y dydx 2х

A: It is double integration problem

Q: 5. y = xArctanx - In v1+x

A:

Q: x" + 2x' + 8x = 2e-2t - e-t,x(0) = 1, x'(0) = 0

A: Given differential equation, x''+2x'+8x=2e-2t-e-t,x(0)=1,x'(0)=0 The objective is to solve the…

Q: 2t + 7 f(t) = t- 3 %3D h(n) = - 2n2-3n+1 %3D f(h(-1)) =

A: Here we have two functions f(t) and h(n), we want to find the value of f(h(—1)). To find f(h(—1)),…

Q: t² - t dt 0, = (x)6 g'(4) =

A:

Q: r²[(x²-y²)²] 1²₂5²² du dt x+y

A:

Q: Find the domain of y = 3x+3. %3D X S-1 O x 2 -1 O x > 1

A: NOTE: Refresh your page if you can't see any equations. . as we know square roots of a negative…

Q: 4+°メ -> X-X %3D dt メ+3

A:

Q: 2) Let T [ ] = DT [₁2 i] = i) 0 ii) 2T = 1 + (-c-d)x+ (-d)²x² + (a + c)³ x³. Then we have: -7 - =

A:

Q: F(2) = | (t + 2) dt. %3D

A: Given F(x)=∫0x(t+2)dt

Q: What is the counterexample of x/x=1

A: Follow the steps.

Q: the differential equati x²y' – 2y = Inx² is cje2* + c2e¯* – x + 5 O c1x² + c2x=1 – In x + ; O 2 +…

A:

Q: EX. Evaluate the JJ(X*+2xy+y") dydx when step size of x = 0-2 and step Size of y=o.5?

A: Given: ∫01∫02x2+2xy+y2dydx with a step size of x=0.2 and y=0.5.

Q: Evaluate [ T 1-x² x² + y² dydx.

A:

Q: Find the linearization L(x) of y = (64+3x2)-1/2 at a = 0. L(x) = %3D

A: The given function is: y=f(x)=(64+3x2)-12 So, f'(x)=-1264+3x2-32(6x)        =-3x64+3x232

Q: Find the initial value of the relation y = 3(x+3)² + 7

A:

Q: O': Find the general yy' – 2y² = e²

A: A first order Bernoulli ordinary differential equation is of the form dydx+pxy=qxyn Where p(x) and…

Q: Find the su x² + y? :

A: The surface is given as z=xy. Take the derivative of the surface, z=xyfx=y, fy=x. The surface area…

Q: If 立= 2t, t-3t dt, then |ü||=

A: To find ||u||^2 from the given integral.

Q: y = v1 - x2 from a = 0 to r = ;

A:

Q: 2x2 f' (æ) = If f(x) = V 1+t° dt, then

A: To find the derivative of integral apply the follow rule

Q: is the minimnurm step of the horno gone ous n What X+ xt 2-X ifferential equatian with its solution…

A: The objective is to find y=x2e-x+x3+x2what is the minimum step of the homogenous differential…

Q: -2 [(x² - y²)²] x+y Evaluate: ³₁² du dt

A: Since the integration is to be done with respect to u and t but the given function in the bracket is…

Q: 2e-0.8t dt, n = 5

A:

Q: 413–2t = 0. 4x dt, then G x If G x -4x Vert-12+3 True False

A:

Q: Solve the dff oq dy 3x寸票-5-2 %3D

A:

Q: X+x- L-X+, dt 2 x²-1

A:

Q: d^2x/dt^2+4dx/dt+4x=7    ;[x(0)=x'(0)=0]

A:

Q: da 9. with #(0) = 20 %3D dt -3 *1(t) = (formulas) x2(t) =

A: We written as the form  x'1x'2=39-1-3x1x2 x'1=3x1+9x2..........1x'2=-x1-3x2..........2 Now,…

Q: -4 3 (x²-y²)²] x+y Evaluate: ₁ du dt

A:

Q: find the first order linear y(t)=4et-1-t-1

A:

Q: Eliminate the arbitrary constant a from the equation (z - a) + y = a O = + 2ry' O = + 2ry Ov =+ 2ryy

A:

Q: 18.t2y′′−4ty′+6y=0,t>0;y1(t)=t2

A:

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.