3x If f(x, y) = e° sin 9y, then fry is given by: O - 27 e3* cos 9y – 27 e3 sin 9Y O 27 eša cos 9y 3x O 27 e3 sin 9y

Q: If w sinxcosy + 1, I = sint, y cost, then by chain rule when t = 7, Select one: O A. 0 О в. - соs(-…

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Q: In Exercises 35–40, find the partial derivative of the function with respect to each variable.

A: Since you have posted multiple questions, as per our policy we will answer first question. Please re…

Q: FIRd the general solution to y'" +(1) y"-12 y-0. None y c, e+c, sin(2-)+c 6 Cy Cos(2 0) y-c, oc…

A: Consider differential equation: a0yn+a1yn-1+.......+an-1y'+any=0 Write auxiliary equation…

Q: 11. (a) y= (x³- 3) * (b) y= VT- 12. (a) Y (b) y = 0' sin 20 1+ 3u 13. (a) v lan y7 (b) y 1. 14. (a)…

A: 11. a) y=x2-3-2    b) y=1-t412. a) y=1+2u1+3u        b) y=θ2 sin 2θ13. a) y=tant         b)…

Q: xは)= 3+ 4 cos ( 2Ont + 36) +, e st'n (60xt)- Yos) Port Wi= 207 W2 = 607 U3= 707 HCF(di , Wz ,Wg) 4…

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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…

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Q: (cos r- sin r) is a particular solution to y" – 3y' +2y = e" sin x = x2 + 3x + 3 is a particular…

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Q: if(r, y) = e sin 8y, then fry is given by: 2z O 16 e* sin 8y O – 16 e2* sin 8y O 16 e2 cos 8y O – 16…

A: Solving differential equations . To solve the differential equations.

Q: Let e4 – sin(x + y²) – VTY. Match the following. A. 4e - cos(x + y*) - | - 2 ay B.-2 cos(x + y²) +…

A: Given,f(x,y)=e4x-sin(x+y2)-xyDifferntiating both the sides w.r.t. x…

Q: The first solution of the D.E. x²y*+ xy+ (x²- =)y=0 is Vi =X Then a second linearly independent…

A: To determine a second linearly independent solution.

Q: Solve the D. E. to the I. V. P. sinx(e- + 1)x' – cosx = 1, y(-) = 0 (1 + e") (1 – cos x) = 2 O (1 +…

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

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Q: Consider the D.E. y(4) + 4y" = 1 - cos(2z). Then a suitable form of the particular solution can be…

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

A: Given differential equation [2x+ycos(xy)]dx+xcos(xy)dy=0. The objective is to find the solution of…

Q: d2s -= -162cos (9t), s'(0) = 9, s(0) = 8 dt2 A) s = -18 sin (9t) + 9 C) s = 2 cos (9t) + 9t + 6 B) s…

A: We need to solve d2sdt2=-162 cos9t,  s'(0)=9, s(0)=8. Now,          d2sdt2=-162 cos9tSubstitute…

Q: Given that y, = 5 cos t is a solution to y"-y'+y = 3 sin t, and y2= 5 e2t is a solution to y" -y'+y…

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Q: Consider the D.E. y(4) +4y" 1- cos(2x). Then a suitable form of the particular solution can be…

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Q: Consider the D.E. y(ª) + 4y" = 1 – cos(2x). Then a suitable form of the particular solution can be…

A: let the non homogeneous differential equation is of the form  y '' + p (t) y' + q (t) y = g (t)…

Q: Consider y(5) + y" = 1+ cos( – t). Then a suit- able form of the particular solution can be written…

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Q: dy for 2xy = dr 4 cos(x) – y?." as Problem 18: A student answers a homework question "Find follows.…

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Q: O y = C1e- Solve 2 y" +2 y' + 3 y = 0 O y = C1e¯i" cos(x) + C2 e ¯ sin(æ) COS C;e * cos(=) + C2 e…

A: Firstly find the roots of auxiliary equation then find the general solution of the differential…

Q: 75 25 75 5. (D+ 1) y = 2cos x %3D V3 Ans. Ce +e2" C2 cos- -x+C3 sin- (-8sin 2x+ cos 2x) 65 6. (D +…

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Q: Consider the D.E. y+4y" 1- cos(2r). Then a suitable form of the particular solution can be written…

A: A linear non-homogeneous ordinary differential equation with constant coefficient has the form…

Q: Given G(x, y) = y* sin(2x) + x²(y10 – cos(y²))" . Find Gyyyxxxy- O a. -192 cos(2x) Ob. O b. – 192…

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Q: Q3 Suppose that w = x² + y² + z² x = e" cos 0 ,y= e"sin0 ,z = re® aw аnd ar aw Find дө

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Q: and its solution EE{ Jm(VAmr) |amncos mô cos( /amict) m=Oh=1 и(r, 0, t) %3 + bmncos m0 sin(VAmict) +…

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Q: Find the general solution of (2x + y cos (xy))dx + x cos (xy) dy= 0 Show your solutions on a…

A: Solution

Q: The general solution of y" (x) – 4y'(x) + 8y(x) = cos(r) + sin(x) is %3D Select one: O a. e2 (c,…

A: We have to find the solution of the differential equation y''-4y'+8y=cosx+sinx. The solution of the…

Q: Find if z = sin(uv)cos(uv), where u = e' and y = e2t. dt %D Lütfen birini seçin: O A. 3e(sin2(e3t) -…

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Q: Problem: dz dz аnd ду Find Əx 1. Z z = 4ex²y3 xy 2. x2+y? ,5,4 3. 2 = cos (x³y^)

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Q: 4.1 z+ cos(T2) dz, z(z² + 1) with C: |z – i| =.

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Q: 21. a. e x = sec sin z sin z) (e sin b. Ve Cos 2sinz 1 U e sin z COS d. cos x √1-e2sinz

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Q: Pls help ASAP ASAP

A: When RHS of a differential equation is of the form H(x)=eaxV  where V is a function of x then…

Q: 2. (a) Determine c, and cz that y = c¿e³x + c2e¯2x + 2 sin x will satisfy the conditions y(0) = 0…

A: We have to determined the value of C1 and C2that y=C1e3x+C2e-2x+2sinx will satisfy the condition…

Q: d2s 2= -162cos (9t), s '(0) = 9, s(0) = 8 dt2 A) s = -18 sin (9t) + 9 C) s = 2 cos (9t) + 9t + 6 B)…

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Q: .2 Q3 Suppose that w = Jx2 + y² + z² e" cos 0, y = e" sin0 , z = re® Find aw and ar aw дө

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Q: The general solution for the Euler DEx?v+y=D0,x> 0, is given by Ody= Cx/2. + C2xInx. O e. None of…

A: We will find out the required solution.

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…

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Q: If z=1+y , I= e' cos(s) and y=e' sin(s), then at (t, s) = (1,0) is as O-2e O 2e O 2e

A: if z=x2+y2 where x=et coss , y=et sins then find ∂z∂s at t,s=1,0

Q: If f(x, y) = e sin 9y, then fry is given by: O 36 e1 sin 9y O - 36 etz cos 9y O 36 ez cos 9y - 36 e4…

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Q: D'y - 40°y - GODY + 288 y = cos (3x) = Cos A. g= C,e* + Czebx + Coe* - sin (a1) + 4 cos (3x) $1 sin…

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Q: The first solution of the D.E. x²y'+ xy + (x² - )y=0 is Vi =X Then a second linearly independent…

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Q: Solve the D. E. to the I. V. P. sinx(e + 1)x – cosx = 1, y(0) = 0 COSX In (1 + cos x) = 1 + e² O (1…

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Q: The general solution of xy" – 2xy' +3y = 0 for x +0 is y = %3D 이미이2e1 cos( In |z|) + c2 sin(1In…

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Q: S sin³x /cosxdx =? O a. cosT cos³z + C 3 Ob. cosr +cosz ) Vcosa + C Oc. 27/2, ) +C Od. (cos*z -…

A: Given: ∫sin3xcosxdx To determine: The value of given integral.

Q: ky and k is a nonzero constant, then y could be (A) 2e*y (B) 2e (B) (C) e+3 (D) kty+5 2. OD OB ョ0 O…

A: 1. dydt=ky and k is nonzero constant.2. dydx=cos(2x)

Q: y(1) = C,e cos() + c,e sin(1) and the initial conditions y (0) = 2 and y'(0) = 1 Determine the…

A: Given: yt=C1e-tcost+C2e-tsint   ...1 And y0=2 and y'0=1   The Product rule: f·g'=f'·g+f·g'

Q: Consider the D.E. y^ + 4y" = 1– cos(2x). Then a suitable form of the particular solution can be…

A: We need to find the suitable form of the particular solution of the differential equation. We will…

Q: 4y" + 8y" — 7у' + 15у%3D0 - A. y = c,e3* + e0.5x (c2 cos x + c3 sin x) B. y = ce3* + e*(c2 cos 0.5x…

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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.