The solutions of the PDE Uyy + 9u = x³e-2y depending on x and y are of the form A) u (x, y) =f (y) e-3r + g (y) e3x 3.x 13e-2y B) u (x, y) =f (x) Cos 3y+g (x) sin 3y+3e-2 C) u (x, y) =f (x) cos 3y+g (x) sin 3y-3e-2y D) u (x, y) = f (x) e ¬3y + g (x) e3y+3e-2y E) u (x, y) =f (y) cos 3x + g (y) sin 3x +6xe-2y

Q: 8. Solve the ff DE y" -9y = 0 y = c₁e³x + c₂e-3x y = c₁ cos 3x + c₂ sin 3x y = ³x (c₁ cos 3x + c₂…

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Q: ³ sin y - 3) = √10 ² Let f(x, y) dt 1 + cos² (t) 16 Then f (2, π/6)=

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Q: cos(2) is equal 1 اخترأحد الخيارات 2-2 sin(z) dy dx dz 2 – z 4-2 r/2 sin(2z) dy dx dz 4 - z z-2 cx/2…

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Q: A. Yp(x) = Ax² + Bx + C, B. Y,(x) = Ae², c. y,(x)= Acos 2x + Bsin 2z D. yp(x) = (Ax +B) cos 2x + (Cx…

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Q: Find the formulation of a particular solution of y" + 3y' +2y = 3+t2 – te-2t cost without…

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Q: The solution of (e+2xy?) dx + (2 cos 2y + 2x?y) dy is given by (A) e + x?y? + cos 2y = c (B) e +…

A: To find The solution of the given differential equation.

Q: Find all. (xo, Yo) in which f(x,y), y(x) =Yo has a solution and a unique solution on some open…

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Q: The solution of (e + 2xy?) dx + (2 cos 2y + 2x y) dy is given by (A) e +x'y² + cos 2y = c (B) e"…

A: Given D.E is (ex + 2xy2) dx + (2cos 2y+2x2y) dy = 0     To find the solution of the given D.E .

Q: Consider the equation 4y" + by' + cy = 0 the constants b,c,m,n are real and different from zero, the…

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Q: |(5e" + 5x4 =. + 9 cos x)dx 5et + x + 9 sin x + c 5ea + x + 9 cos x + c 5e + x³ – 9 sin x + c O et –…

A: Need to find integration

Q: 2) z(x, y) = (x² + 5y)³ (3y + 2x)

A: Let's find dz/dx and dz/dy.

Q: a) Solve (6x²e* ,x0 ii. [3 cos 2xsin 7xdx 2x+1 1 10x +5 b) Show that (x² +1)(2–x) Hence, find | 2-x…

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Q: 7) Consider yu- 3y' -2y= 3t cos(t) a) Find the complementery solution, 6) Fnd the par ticuler yo e…

A: Given differential equation is  y''-3y'-2y=3tcost we have to solve this.

Q: Match the graphs with their parametric equations. I O (a) x=4-t+2, y = ² O (b)x= 2 - 3t, y = √t O…

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Q: The solution of (e® + 2xy²) dx + (2 cos 2y + 2æ?y) dy is given by (A) e + x²y² + cos 2y = c (B) e+…

A: Answer:- The solution of ex+2xy2dx + 2cos 2y + 2x2ydy          —       (1)

Q: . Can the equation x + y + z = sin(ryz) be solved uniquely in form = f(x, y) in a neighborhood of…

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Q: 4. Suppose the following functions are a general solution of: y(4) + azy" + azy" + a13 + a0y = 0…

A: The differential equation is y(4) + a3y''' + a2y'' + a1y' + a0y = 0 We have to find a0, a1, a2 and…

Q: 19) For the ODE x(t) = e²t (c₁ cos(√3t) + c₂ sin(√3t) − sin (3t). cos (3t), let y = x' and 37 Y=…

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Q: The equations xe + uz – cos(v) - 2 = 0 and u cos(y) + 5x?v- 7yz2 - 1 solved for (u,v) as functions…

A: Given equations are xey+uz-cos(v)-2=0                  (1) and ucos(y)+5x2v-7yz2-1=0           (2)…

Q: ut = 2uxx осхез ux (0₁ t) = Ux (3₁ t) = 0 cos. U (x, 0) = 4, COS 2 TX - 2 cas y mx TT t>o

A: As multiple questions are there and it is not mentioned that which question to be solved, I will…

Q: 32) Find ур(0) for the equetion y (4) - y" - 2y + 2y = 3xe³ + cos x

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Q: 1) [sex² 4x² - x² dx 2 dx 2 ਤੇ 3) sex² (4x+²) dx 2) 4) S X dx √4-9x² using Integration by…

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Q: Can you explain how all A B C D terms are calculated

A: Solution of the given question is like as

Q: The PDE ugy + sin(y) u, = cos(y) Can be reduced to a first order linear equation as: A) uz + cos(x)…

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Q: Solve: (2x cosy + 3x y) dæ + (x – a? sin y – y) dy = 0 O 2x cos y + 2x2y-y = C O x3 cos y + x?y-y =…

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Q: (7) Show that the given functionis an integrationy factory Solves a) Sinydx+ Cosydy =0(e),…

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Q: 5. Find L{f(t)} a. f(t) = sin?(t) + t b. f(t) = n² – 8e¬2t + (et + 1)² | c. f(t) = F, sin yt -cos…

A: As per our limit we can solve only first three subdivisions if you want the answer for other…

Q: a. Find the general solution of (D² + 4)y = 0. y = C₁ cos2x+c₂ sin 2x y = C₁ cos x + C₂ sin x…

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Q: Exact DE Try these! Solve the following equations 1) 2(y + 1)e*dx + 2(e* – 2y)dy = 0 dy 2) 2xy + y2…

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Q: 4. Consider a3(x)y"" + a2(x)y" + a₁(x)y' = 0 (a) What's one trivial solution? (b) Suppose the…

A: Please see the attachment

Q: What is the general solution of (Dº + 20D4 + 100D²) y = 0 y = C1 + C2a + (C3 + C5a) cos V10x + (C4 +…

A: The given DE is: (D6+20D4+100D2)y=0...(1) which is a linear homogenous differential equation.

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.