Particular Solutions - D-Operator Method 2 15 2 L 1) .. 40- - 1, " ū + 02x LY re 19. (D²+3D+5) y = 5e-* sin 2x

Q: Ou :? u =x +y +:, x=e" cos 21, y =e"21, : =e" = e" (cos 21-sin 4t +&t +8) +2e Ob. e (cos 21 - 2 sin…

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Q: 2. A ball is rolling around on a surface with shape given by z = f(x, y) = e-5y sin²x. The ball…

A: (a) To calculate the direction in which the ball would roll from a general point (x, y), we need to…

Q: y" +2y = 2x+5-e-2r y""-6y"=3-cosa

A: These questions are about ordinary differential equation.

Q: dx Xex+10, Complete the Square.

A: Given,          ∫1x2+6x+10dx

Q: How did he get the value inside the circle f(x, y)=x² + sin(xy) Vf=x*+sin(xy)) i+ d(x²+sin(xy)), dx…

A: given ∇f(1,0)=2i+j we have to find the direction in which the directional derivative has some value.

Q: Use separation of variables to find a product solution to the following: d²u du -u, k>0 dr -U= dr² k

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Q: ) (x² + y³ )dx+xydy= 0

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Solve the equation 4 x² y" + 4 x y' – y = 0

A: The given opinions and incorrect. There can't be x in power. In particularly x(-x/2) can't be…

Q: Solie The equahins - 3 )X Ce O Cx-j) ( cy - dy ) = 0 3 (zay- Sin n)olx + (u"- Cay) oly > o (2y-

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Q: The indicial equation of (-1) y"+ (-1)y'+2u 0 at r=1 is: (A) + 2r +1=0 (B) r1 2r = 0 (C) r-r= 0 (D)…

A: Given differential equation is (x-1)2y"+(x3-1)y'+2y = 0

Q: 2(s+1) What is L¯' s- using Completing the Square? + 2s +10 А. 2e cos 3t 4 -e sin3t 3 В. 2е сos 3t…

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Q: -1 du 4) [cot-u] %3D 1+u2 dx dx d 5) 1 du [sec-1 u] %3D dx u vu2-1 dx -1 du 6) [csc-1 u] dx u vu2-1…

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Q: ) 3(x+ y) dx + x(x*+ zy + uy) dy - o t.

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

Q: Solve J²u = Ət² u (0, t) = u (x, 0) = J²u 4- 2 მ2 u (π, t) = 0 sin (2x), 0 0 (x, 0) = 0 Ju Ət

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Q: B dy x/1-y2 dx 1+x2 II

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Q: The equation (tan²x+3y²)sec²xdx + (3tan²x + y²)dy=0 can be solved by

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Q: 1. S x+cos 2x dx x2+sin 2x 2. Sxe**(ex² + 1)'dx

A: According to the definition of definite integrals, if dFdx=f(x), then ∫f(x)dx=F(x). In this problem,…

Q: 2. у" — у' — х %3D 0

A: To solve the given differential equation.

Q: Solve the following 1 1) y dx + x² + y? dy = 0 x +y 2) (3x? In x+ x² –y) dx- xdy = 0, y(1) = 5 dy…

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Q: ) (2ху — tanу)dx + (x* — хsec*y)dy 3D 0

A: Given: (2xy-tany)dx+(x2-xsec2y)dy=0

Q: — хz + 2ху %3 0. xy ay az az Solve, y? ax

A: Lagrange's Method: Let us consider a standard form of the first order partial differential equation…

Q: Q4) Use separation of variables method to solve: d²u ди ax² + =u where u(0, y) = 0 and ду du(x,0) by…

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Q: Solve (a) xy" - 3y' = x², (b) yy" + 2y'2 = 0, (c) y" + 4y = 0,

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Q: -2x Use Green's Theorem to evaluate [(3 ye^²* − 7 sin² (3x³)) dx + (5x² + 2x²y² +8e³¹²-7x+²) +2) dy…

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Q: Use separation of variables method to solve: ди ổn ôn + =u where u(0, y) = 0 and ду Əx² du(x,0) ду =…

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Q: The equation of a circle can be represented as in-h)² + (y – k)² = r², where (h. k)ie center of the…

A: Substitute h,k and r in the equation, x-h2+(y-k)2=r2 and solve for y to yield the result.

Q: d) 3xy" +4y' +y = 0.

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