1.3.1 Problems. I. Integrate by Guess-and-Check. 1. /хех dx. e5x Answer. x 5 e5x + с. - 25 2. Гx cos 2x dx. sin 2x cos 2x Answer. x + 2 +C. 4 3. S(2x + 1) sin 3x dx. cos 3x Answer. -(2х + 1) 3 sin 3x + 9.

Q: Solve the following initial value problem. y) = -3 sint+2 cos t with y"'(0)= 9, y"(0) = - 2, y'(0) =…

A:

Q: 3. Obtain in two ways the general solution of (r + sine - cose ) dr + r (sine + cose ) de = 0

A: Use substitution method

Q: 3 S² x³ cos x ²dx 6.

A:

Q: 5- for y = (x² + 1)5 dx a)10(x² + 1)5 b) 10x(x² + 1)* c) (x² + 1)* 6- Sin 2x is equal to: a) sin x…

A: Answer of the above questions are

Q: 1. f(x) = In 5x 2. у %3D 103х Final Answer: Final Answer: 3. y = sin(e3*) 4. y = cos 2x (e*²-1)…

A:

Q: Find the iterative scheme for the root of equation cos x- 3x+1=0 by Newton-Raphson method. O a. None…

A: Newton rephson method problem....

Q: 10 L-1 e2s [(s + 3)4 + 13(s + 3)² + 36| sin(2t 글e-3+0u(1-2) (Mn2 sin(3t)) - 2e-21+6u(t – 3) (sin(2t…

A:

Q: 6. Solve y sin (x) cos (x) with initial condition y'(7) = 1 and y(7) = 0.

A: y = 1/4 [ x - 1/2 sin2x] +x -π/4

Q: 5 dr dy Suppose x and y are functions of a third variable t. If sin²(x) + cos²(y)=- and dr - 2, what…

A:

Q: Use the method of undetermined coefficients to solve the initial value problem. 33 y ==cos2t 10 33…

A:

Q: Solve the initial value problem. 33) dy - et sin (et – 5), y(ln 5) = 0 dt A) y = sin et - sin 2 C) y…

A: Given initial value problem can be evaluated as shown below by using substitution method

Q: 2.L cos v5t 3V5 sin v5t 5 8s – 3 a. s2 +5 8s + 3 b. 52 +5 8s – 3 2-5 С.- d.none

A: NOTE: Refresh your page if you can't see any equations. . use the Laplace rule

Q: The particular solution of the following equation by using the method of undetermined coefficients 2…

A: A detailed solution is given below.

Q: Suppose that x2y" + axy' + by = 0 has the general solution of the following form: y = x-(C, cos (3…

A:

Q: If e 17/2- 2i =sin2 then z = %3D - 2i In(sin2) + 4kn -2 In(sin2) + 4kT - 2i In(sin2) – 4kn 2i…

A: Concept : eiθ =cos(θ)+i sin(θ)                  if θ=2kπ                    ei2kπ =cos(2kπ)+i…

Q: (a) To determine To compute: The initial value problem + 4x = sin 4t with initial conditions x (0) =…

A: The given differential equation is: d2xdt2+4x=sin4t, a) for x(0)=0, x'(0)=v0>0 we have to find…

Q: Solve the initial value problem: y'+2y = 40sin(t)+cos(t),      y(0)=6

A: Given,y'+2y = 40sin(t) +cos(t)y(O)=6

Q: 1 =dx = V81-(3x+5)? 2 3x+5 -tan- (***) + c 9 o 음sin-1 (3g5) +c 9 o tan-! (**5) +c o sin-l (초5) +c…

A:

Q: 3. General solution of (ylny - e-xy)dx + ( + xlny) dy = 0

A:

Q: Find the solution. y' = 5y + e 2x y2, y(0) = 2 139e 15x – 3e -2x )1/3 A) y = 17 39e* - e-2x )1/3 B…

A:

Q: The particular solution of the following equation by using the method of undetermined coefficients 2…

A:

Q: 4. Solve the initial value problem 8 + 3y = , e > 0, y(n) = -5. sine %3D de

A: To solve:  Initial Value problem  θ dydθ + 3 y = sinθθ2  The given Differential equation can be…

Q: 1 Find L -1 s²+4s+8] A)늘e-2t sin 2t B)- e2t cos 2t c)e-t sin 4t D) e2t cos 4t

A: Formula Used:L{eat sin(bt)}=b(s-a)2+b2

Q: The solution of the equation below can be represented as s y(x) = yn(x) + yp(x). y"+y' - 2y = e-2x +…

A:

Q: 3X 7- (0²1)y=K²" yp-e (4X-3} 8-(0-20+4)y=x+3x-5x+2 yp=Dx yo= 3.2 -2K 2. to-(D²+2}y=x²+xre+cos3X éte…

A:

Q: 2x 2)/3x* 2) [3x* - 9x² +1 V9-x² dx .2 3) [ sin xcosx dx x cos.x 4) S sin² xcos 4) sin x cos x dx

A:

Q: 1. Eliminate the arbitrary constants on the given equation: -3 x sin y - x²y³ = C

A:

Q: too ·00 dx COSX x² +hx+5 =le Residue solution cos (2)

A:

Q: 9. cos (2t) dt 10. " sin?t cost dt /2 11. sin'x cos?x dx 12. (2 sin0)² d®

A:

Q: 8. Solve the initial value problem: 1 dy + CoS I – 2xy y(y + sin x), y(0) = 1 1+ y? dr

A: Given: The given ODE equation is 11+y2+cosx-2xydydx=y(y+sinx),     y(0)=1

Q: (1) x(x + 2)² dx x-x² (3) 4+x² dx e²x (2) 2) 14+720x dx J ex (4) | sin³2 sin³2 x sin 2x dx

A: According to bartleby guidelines when student post more than one question then expert must have to…

Q: 1. f(x) = In 5x 2. у %3D 103х Final Answer: Final Answer: 3. y = sin(e3×) 4. у %3 cos 2x (e**-1)…

A:

Q: a. Solve the initival value problem: y = 5 cos (2r)/(6+ 5y), y(0) = -1. -6+V36 - ( sin (x) + 10 2. A…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 9. Find the value of k so that (2y sin x cos x - y+ 2y²e")dx - (x- sin? x+ kxye*)dy = becomes exact.…

A: To find the  value such that given equation is exact  differential equation.

Q: 35) y = -4 sin x 4+ 2+ 2n -2+ -4-

A:

Q: 51²e-31 – e121 cos 8t 10 (s+3) 3-12 (১-12)-64 10 s-12 ((-122+64 (s+32 10 (s+32 s-12 (-127-64 10 s-12…

A: lets see the formulas we are going to use here L{ tneat } =n!(s-a)n+1               ⋯⋯⋯(i)L{ e-at }…

Q: 2/solve the differentialequation by using methad af Variation of (complete salution is vequired)…

A: Given equation is y'''+9y'=1cos11x               (i) Let us consider y'=z. Then, eq. (i) is reduced…

Q: Q-4) Find the general solution of the Cauchy-Euler equation x'y"+ xy'+4y = sin(In x)

A: Solve the Cauchy Euler differential equation

Q: 5 dx 3 dx, x> Find V25x-9 0 sin 13x+c -13x+C InV1+9x +3x +c 5x 25x2-9 in 3 + C 3 In 5x 25x2-9 + C 3.…

A:

Q: Find L{(t- 2) (3 cos 5t + 1)}. COS 3(s2-25) (s²+25)? 30 | s2 s2 +25 6. 3 g3 s2 s2 +25 s(s² +25) 6s…

A: Find the Laplace transform of  L{(t-2)(3cos5t+1)}

Q: 1. L(e** + e¬* + x²) S-4 s+1 s3 e3 2. L(sin 2x + e²x+3) : 2 + s2+4 s-2 Hint: e2x+3 = (e2x)(e³) %3D…

A:

Q: 4. For any angle 0, Therefore: sin (0) = cos(0 - π/2) cos(0) = sin(0 + π/2) sin(0) has a phase shift…

A:

Q: 1. f(x) = In 5x 2. у %3D 103х Final Answer: Final Answer: 3. y = sin(e3×) 4. у %3 cos 2x (e**-1)…

A:

Q: 13) y = 4c°(sin 0 – cos ) A) 8e® sin e B) 0 ) 4e0(sin e – cos e) + 4e® D) 8e®(sin 0 – cos 0) 14) y =…

A:

Q: Solve the initial value problem y′′ + 9y = cos(3x)+sin(3x) for y(0)= 2, y′(0)= 1.

A:

Q: 4 sin 18x + 8 cos 9x dx. sin? 9x + 2 sin 9x + 5 Q10: Determine 4 А + C 9 In sin 9x + 2 sin 9x + 5| 4…

A:

Q: dz 1. Vz? + 6z + 5 wdw 2. (csc 4w? W3 - 4 sin² 4w² ydy 3. 4y4 -8y² +1 ds 4. 4sv3s° +16 3* dx 5. V9x…

A:

Q: Solve the initial value problem 8 cos(8x) »y(0) = –1 3+ 2y and determine where the solution attains…

A:

Q: Solve the initial value problem y' = 4 cos(4x) 3+ 2y , y(0) = -1 and determine where the solution…

A: Given IVP y'=4cos (4x)3+2y , y(0)=-1