sketch the odd and even extensions for -3,3]. Use the substitutions : '= ye¯* s = x Q.3 to solve the ди PDE : + y = x, u(1, y) = cos y. ôy

Q: 10. Show that 2" + 42' + 8z = 0 if z = e-2=(sin 2x + cos 2x).

A:

Q: cos 2t dt 2.

A: Given:             ∫-π3π31-cos 2t2 dt Take the constant out: ∫a·fx dx=a·∫fx dx…

Q: Find general Solution of DE =0 on Co, mo). AISO how that xJú (x)-VJ,(x) + x Cn)

A:

Q: 2.3 Find the general solution of p fanx+q tany =lanz

A: Given:   P tanx+q tan y=tanz→           1   is of the form pP+qQ=z:

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: . Use Regula-Falsi method to find solutions of x = cos x which is accurate to within 10-8 . Take x,…

A:

Q: Find z in 2= Sinh (4-j5). cos (4-5) express in polar porm

A:

Q: 2. Show that u(x, t) = cos(x – ct) is a solution of Ut + cuz = (0

A:

Q: Suppose tan u = %¾ (sm u>0) and tanuo12/5 Ccasx cO]. Ead he exsee velos OR the followly trgeronetnc…

A:

Q: -3t 10. s = cj e" + c2 e" cos 51 + cz e" sin 51 + 123 O Sm + 5 Su + 17 s - 123 s = 100 O Sm + 17 Su…

A:

Q: If xty= 2e Cos Øand x-y=2ies.m Ø show that Su

A:

Q: sin (2t + 1) - dt cos? (2t + 1) 31.

A: Use trigonometric substitution method for solving the integral.

Q: The integration expression + 4)cos(3ln(x) +4)dx must be transformed into using suitable choice of…

A:

Q: iii) E(-1)"+1 cos²(÷) COS n=1

A:

Q: 5 Evaluate the integral 2x cos(xy)dydx 4 0.

A:

Q: What substitution should be used to solve the integral x²dx |4+9x² O sin u=3x/2 sec u =2x/3 O sec u…

A:

Q: Solve ", = c²u«» 0sxS1, t20 subject to u (0, t) = 0, u(1, 1) =0 for all t u (x, 0) = 0, u, (x, 0) =…

A: The general solution for the homogeneous wave equation…

Q: Solve the given differential euation: dr/dθ+rtanθ=10cosθ. 1.r=(10θ+C)tanθ 2.r=(10θ+C)cosθ…

A: In this question we have to solve the given differential equation.

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: Find a general solution of each reducible second-order differ- ential equation y" = 2yy'

A: Recall the chain rule of calculus:

Q: Show that cos 3x = 3x has a solution in the interval [0, 1]. Hint: Show that f(x) = 3x – cos 3x has…

A: solution:-f(x)=3x-cos3xapplying intermediate value theoremintermediate value theorem states that if…

Q: 7). Suppose a is a positive constant less than T. Prove that the equation 2x+cos x = a has a real…

A:

Q: 4. A force of F(x) = x - cos(3x) + 2,x is in meters, acts on an object. Identify the work required…

A:

Q: Evaluate the integral. 5n /2 2, 1 - cos t dt 3π/2

A: ∫3π25π21-cos2tdt=∫3π25π2sin2tdt=∫3π25π2sintdt=∫3π22π-sintdt+∫2π5π2sintdt=1+1=2

Q: Evaluate the integral. 1 cos 2t dt 2 7x/2

A: To evaluate the given integral.

Q: Evaluate the integral. sin (8t + 16) dt cos (8t + 16) sin (8t + 16) dt = cos (8t + 16)

A: Solved below

Q: Find a differential operator that annihilates 4e2" cos 3x + 3x²e5.

A: Let L be the differential differential operator that annihilates 4e2xcos3x+3x2e5x. Find L.

Q: Compute e4 cos (r – 3) dr with two decimal places. Number

A:

Q: 11. Find the general solution of uyy - 4xu, = cos 2y – 2x sin 2y + 4x.

A:

Q: Obtain the General Solution of: (z + 2)* cos yudz - [sin y In(3z 4 6) – d

A:

Q: Find the general solution of the differantial equation given by www |y" – 4y' + 5y = 3xe* – cos2x +…

A: Given y''-4y'+5y=3xex-cos2x+x+1sin2x

Q: Show that y1(t) = cos(3t) and y2(t) = sin(3t) are linearly independent for all t

A:

Q: Integr S√₂-cod -1 ation fuctions. 1-cos²x) dx Not of the above B 1 O

A:

Q: 2. A. If : = sin(3x+2y) , verify that 2 -3 = -6z ax2 B. If f = x³y3 + 2xcosy + y?lnx then show that…

A: x=sin (3x+2y)

Q: Ti Ti to 8 Integrate cosh(4z) dz, C any path from - 8 Use the first method, if it applies, or use…

A: Using:- sinhx = -isin(ix)               Sin(-x)=-sinx               Sin (pi/2)=1

Q: 19. Find potential function for = (3xy, æ³)

A:

Q: find do diy y = (cos(x))*os)

A: Given y=(cos(x))^(cosx) Now differentiate y with respect to x

Q: az Use an appropriate form of the chain rule to find dt 1 z = 2 cos x sin xy; y = 5t t Enter the…

A: z=2 cos x-sin xy ; x=1t; y=5t   see z is a function of x and y ,where x and y are functions of t so…

Q: Can you help with this problem step by step?

A: Given integral is

Q: Find L {(2 – t) (5 cos 3t – 1)}. 1 g3 10 + s2 +9 - - s2 s(s²+9) O 1 s3 10 + s2 -9 2 - - 8(s2 –9)…

A:

Q: Find (1,0) where y2 + x2 + eV = 0

A: Given y2+x2+ey=0 ⇒y2+ey=-x2⇒ddx(y2+ey)=-ddx(x2)⇒2ydydx+eydydx=-2x⇒dydx(2y+ey)=-2x⇒dydx=-2x2y+ey

Q: - 2+j= 5 Z153°.435, 3+ j2= V13 Z33°.69, and 1– j2 = /5 2-63°.435 (1 – j2) (-2+ j)(3+ j2) = 1.386…

A:

Q: Find 2 if x? cos4 cos* T. 1) 2xcos x+4x2cos3xsinx 2) 2xcos x- 4x²cos³xsinx O3) 2xsinx sin xcosx 4)…

A: Hence option (2) is correct.

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: if we let u-4x- 1 for the 2 tan(4x-1)-3 cos (4r-1) dx, what will be the resulting integrand? cos…

A: The given integral is  (2tan(4x-1)-3cos2(4x-1))/cos(4x-1).

Q: Evaluate the integral. sin (6t + 17) -dt CoS 2 (6t + 17) sin (6t + 17) dt%3D cos 2 (6t + 17)

A:

Q: find y prime and y double primey=cos(x^2)

A: To apply chain rule and product rule to find the first and second derivatives of a composite…

Q: Find Z in (1-j5) 2= tanh cos lat5 express in lagarithm Form

A:

Q: The integral (cos(3x)) sin(3x)dx under the change of variable u = cos3xbecomes v uz du. -9/29 Select…

A: Given,

Q: Calculate the given integral: S3 sec“(10x) dx 3) o함n a) O - tan (10x) + 3 tan(10x) + 3x + C 10 1 3…

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.