Let e4 – sin(x + y²) – VTY. Match the following. A. 4e - cos(x + y*) - | - 2 ay B.-2 cos(x + y²) + 4y2 sin(x + y?) + 4(xy)3/2 C. -2y cos(x + y?) – 2 xy y? D. 16e4z + sin(x + y) + 4(xy)3/2 select 1. fz select - 2. fu select 3. frz select - 4. fyy

Q: Choose T or F* y"+2y' +5y = cos(3x)-sin(3x) ( True Fouls Yh=c1 cos (2x)+c2sin(2x) yp=A cos (3x)+ B…

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: Find the particular solution : y" + y' + 16y = sin4x 1 (а) Ур — — 4sin4x (b) Ур 3sin4x --cos4x 1 (c)…

A: Correct option: C The detailed answer is listed below, kindly do like it if you find my answer is…

Q: 0 ex) メzx-3 معارره اماسرجعادكالعودعل الماسن عنz=لا x2. xy- yーx find %3D 3 t Fcx)こx+5X+2 Find f cl Q…

A: (1) f(x)=x3-2x2-3 Find f(x) at x=2 and f'(x) at x=2 (2) x2-xy2=y3-x3 find dydx (3) f(x)=x2+5x+23…

Q: Consider the following IVP: y" +y' = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x) =…

A:

Q: The general solution of the DE y"+ y = x is def ined by (y= C¸ cos(x ) + C¸ sin (x) +x 2 (y=C¸ cos…

A:

Q: 14. Find the antiderivative of 5sinx In 5 cosx. a. 5cosx +3 c. 5sin x In b. 5sinx-2 d. 5 sin x + 7…

A: Anti derivative of the function

Q: B\ Suppose that = 4 cos? t , x = v3 sin(2t) and 0 < t < n. S d²y *= - tan(2t) and = -sec (2t). 1 dt2…

A:

Q: Find an antiderivative of the given function. 4 cos 9x O A. sin 9x O B. - 36sin 9x O C. sin 9x O D.…

A:

Q: 21 40 JJJ. 7yz cos(10x5) dv, where E = sin (2) X = {(x, y, z) | 0 ≤ x ≤ 1,0 ≤ y ≤ x, x ≤ z ≤ 2x}

A:

Q: ) Evaluate A) /16 /2 cos (167 x5 ) dx dy. Os xs 2 Og y s x*

A:

Q: dy Find ax eby = cos (8x +y) Select one: A. -8 sin (8x + v) 6e6y + sin (8x + y) B. sin (8x + x+y)…

A:

Q: If f cos42t dt = At - B sin 2t cos 2t + D sin 4t cos 4t + C where A, B, C and D are constants, 2A-3B…

A:

Q: Evaluate the following integral. T/2 1 1/4 . sin TX cos 2y sin 2z dy dx dz 0 0 0 T/2 1 1/4 sin TX…

A:

Q: Consider the non-homogeneous O DE y +2 y +2y = sin 2x using undetermined coefficients method, the…

A: Given differential equation is y''+2y'+2y=sin2x To find the Particular solution yp of the…

Q: 8)find dy/dt for y=cos^2(3#t-1) # is actually pie or 3.14 etc I just don’t have the symbol on my…

A:

Q: (D2 - 3D – 4)y = -8e'co s 2t 10 2 а. Ур e*cos2x + e*sin2x %3D 13 13 b. y, =e*cos2x + 12 e*sin2x 13…

A: The given problem is to find the particular solution for the given non homogeneous linear…

Q: The general solution of sin (x)-cos-(x)3cos(x) is: a. x=2km b. x=TT+2kTt, x=±+2KTT c. X=2kt, x=±+2ka…

A: Given  sin2x-cos2x=cosx Use trig identity sin2x+cos2x=1…

Q: What is the trial particular solution for g (x) = (x2 – 1) sin 2x? | O Yp (Ax? + Bx – C) sin 2x +…

A:

Q: rION 4. Find du/dt for the following: 35. u = tan-(xy) ;x = sin t;y = sect x-y 36. и 3D In ;x = sec…

A:

Q: 1. a. Let In = exp (nx) sin (exp (x)) dx. By making an appropriate substitution, or otherwise,…

A:

Q: 4. a. Show that for 0 Va² + sin² a. b. Generalize the result in part (a).

A:

Q: For the following integration / sin"(24x) cos(24x)dx what is the suitable substitution? a.…

A:

Q: Evaluate: 4S d sin(t?)dt dx x 3x²sin(x“) – sin(x²) b. 2x°cos(x°) – 2xcos(x²) a. 3x²cos(x^) – cos(x²)…

A:

Q: Match the following guess solutions yp for the method of undetermined coefficients with the…

A:

Q: 2. If y = C₁ cos2x+C₂ sin 2x+2sin x is the general solution of a certain nonhomogeneous LDE, which…

A: The given general solution of non-homogeenous  LDE.  y= c1cos2x +c2sin2x +2sinx   We have to find…

Q: the following is the general antiderivative G(x), for g(x) = 2 sin(x) + 12e³x + 2√x ? ternative: 1…

A:

Q: | 1. Find dx dy for the following functions : 45) y=x' log,(3– 2x) (ans.:3x² log,( 3 –2x)-73-2x…

A: We have to find the following derivatives

Q: day Find y, of 2+ + 6y = 51 cos 3x. ... a.) y, = - cos 3x + 4 sin 3x b.) y, = cos 3x-4 sin 3x c.) y,…

A:

Q: Show that where n is a positive integer.

A: To show

Q: If z = x2 – y2 and x t cos 2r and y = r sin t, then %3D a2z is ar2 (A) 2 cos (2r) + 2r? cos?(t) –…

A:

Q: 1. Find for the following functions : dx 4i) y-bmcx* +2y}kos x (ans.: 4x.cos x - 2 In( x² + 2 )sin x…

A: To find the dy/dx of  y=[ln(x²+2)²]cosx

Q: 7 (a² +b°) 1 Prove that : dx = ở (a sin x+ b° cos² x)' 4a’b?

A:

Q: What is the general solution to the DE, !! dt 2? - 2x + 2? What is the general solution to th O In…

A:

Q: Solve the D. E. to the I. V. P. sinx(e¬ + 1)x' – cosx = 1, y(곡) = 0 - O (1 + e') (1 + cos x) = -1 O…

A:

Q: Find the dy + 9 Cos Cx)= 3 Cos Cx) paihular suluhon Of the differenhal epeccin sahisfying the mihal…

A: Topic- Differential Equation

Q: I. Evaluate the following Definite Integral. 1.) L,9 6x3+4x2-8x dx 2.) x²(2x³ + 1) dx 2x 3.) sž…

A: Integration

Q: 4y" + 36 = csc 3x y- C, cos 3x + G, sin 3x +; (sin x - cos x) – 4x e y = C, cos 3x + Cz sin 3x - x…

A:

Q: Q4. Given that: z = y sin(2x) + (1+x²)e* + cos x tan-1(y* + 1) In(y6 + 137)

A: Given that, z=y sin2x+1+x2ex+cosx tan-1y4+1 lny6+137 ∂z/∂x is the partial derivative of z with…

Q: Find the general solution of the DE: dyldx = sin(7x) cos(5x) + cos(7x) sin(5x). O y = (-1/12)…

A:

Q: 17. (D+ + 2Dz + 1)y = 5– 3x2 a. y = (C, + Czx) cos x + (C3 + C4) sin x – 3x2 + 17 b.y = (C1 + Czx)…

A: As per the company's guidelines we are supposed to solve first question for you, kindly repost other…

Q: Н. W.4 Find dy/dx for the following : 7) y = 3ln (sec2x) eln(cos-1x²) sinx csc x) 9) y* = sin-1 x 1)…

A:

Q: 3. Given that 2 = 6²¹ sin (u + ), e2v Use chain rule to find az/0x when x = 0, y = 0. u=e¹ - sin (y…

A:

Q: Following S sin(A) cos(B) dx = ; f sin(A + B) + sin(A – B), | what is the integral of f sin 5x cos…

A: We have to solve the following

Q: If it was f(x,y)=y cos(6xy) SO a² f Əy² 2² f Əy² a² f Əy² a² f Əy² = 36 x²y cos(6xy) + 12x sin(6xy)…

A: A detailed solution is given below.

Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. @ y(x)…

A: We find the general solution of given DE  y"+y'=-cos(x)........(1)

Q: Differential Equation Activity

A: To find the general solution of the given differential equation

Q: Find the solution to the following PDES: ди ди y ду Ans. u = C;(xy): X dx k 2 dx- ди k > 0 at Ans. u…

A: The given problem is to find the solutions for the given partial differential equations.

Q: 0.5 COS T - In(4 sin z) dz. J0.1

A:

Q: 8. Which of the following is the solution of * [2x + ycos(xy)]dx + xcos(xy)dy = 0 x? + cos(xy) =c x?…

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.