Find the seneral solutionn given the Condrhors y'+2リ=0 JO) - y(277) y'o) = y'em) ノ

Q: Solve y" - by'tlly - Slt-1), ylo)= 1, y'lo)=0 ylo) = |

A: The given function is  y''-6y'+11y=δ(t-1) The initial conditions are, y(0)=1, y'(0)=0 We find the…

Q: dz at the point (3,2, 1), where z is defined implicitly by the equation z +z²x² – y = 8 Calculate dx…

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Q: 2) vting daplace toansfóöre, Solve x" Zt)+4x'Lt)+3=(4) uing = 10 gint yeren that xco) = -3t Ans: ILt…

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Q: Solve the equations: a) y"+4y'+4y=0 dy 3 b) - ²y=x dx

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Q: Assume that n(U)= 85, n(A’ intersect B’)= 19, n(A’ intersect B)= 22, and n(A intersect B’)= 23. Find…

A: Given that n(U)=85, n(A'∩B')=19,  n(A'∩B)=22,  and n(A∩B')=23. We need to find, n(A∩B) and…

Q: 6) —— (y² + z²)u₂ +xzu₂ − xyu¸ = 0

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Q: If x = u?(u? - 1)2 and y = (3u2- 1)2, then what is the value of dy/dx? A none of the given choices 3…

A: I am attaching image so that you understand each and every step.

Q: FIND 2 DIFFERENT (LINEARLY INDE PENDENT) POR THE D.E. SOLUTIONS y"_x² y'- 3xy = o 2.

A: The linear homogeneous ordinary differential equation has the form pxy'' +qxy' +rxy=0. If the…

Q: еху (ay cosica) since) -y + ay²e²) dx = ) dx = (x - 5.n²cx) - 4xye Ja

A: Exact differential equation Mdx+Ndy=0 [ where My=Nx ] has the solution. ∫M (taking y as a…

Q: ху'- у - 5х1 — Зх? + 2х %3D 0

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Q: Uindaterraind coefdicients y" t 4ytuy = (3+x)e"; yro)=2, y'6) =5 %3D

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Q: d²(x²+2xy+e» - 4) dxdy

A: Given To evaluate-4)d2(x2+2xy+ey)dxdy

Q: y' + E) y = xy? 2

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Q: y' = *+y2 ху

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Q: х — у—1 3y – 3x – 3y (1) = 1 у (1) %3D 1

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Q: d y then is dx? x=1-8t Suppose y = 5t* +2

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Q: If y=t3, then y(6)+y(5)+y(4)+(1/3)y'=y? What is the power of y? a) 0 b) 2/3 c) 1/3 d) 3 e) 2

A: Differentiation of y with respect to t can be given as:

Q: y'47y'+12y = 2le", y(0)=,0)=-10 .

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Q: By substituion, u=(y/x) in equation xy'=(x2+y2)1/2 we have u'*x+u=(?)1/2. a) u b) u2 c) 1 d) u3…

A: Substitution in differential equation

Q: 7.) Solve а) y'+y'-by=0 6-) у"-ну' +13y=0 с.) у" -бу' +ац=0

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Q: 4. Classify and reduce the following equations to a canonical form: (a) yu -x*u, = 0, x>0, y>0. (b)…

A: To classify and reduced in canonical form of the given equation is..

Q: 4yy" + 2y' = 0 = y' =? A) y'= -In B) y' = In c) y' = 2n(cy) D) y' =-In E) = 4 1n

A: Given that 4yy"+2y'=0

Q: If the point A (4,3) and B(x,5) are on the circle with centre 0 (2,3). Find the Value of x

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Q: 2 a) Solve x y'= (2+ yx)·

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Q: Solve as simply as possible: J²u Ət² with u(a, , t) = 0, u(r, 0, 0) = 0, and 9 (r, 0, 0) = a(r) sin…

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Q: a) Find dz, if z = e' sin e %3D b) Verify uxy = uyx , if u = In /x² + y² . %3D

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

Q: 5. y"+9у-0

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Q: g Solve Rour of the following D.E A)(xュ)dx + 2xy dy dy B) ャリ=ex c) (xx v y'es )dx -(y- )dy zo D) (X…

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Q: Solve for Linear DE of Order n: y′′−3y′+2y=cos(e^−x)

A: Using General Method of Linear D.E.

Q: 1 b)y" + y = ; 1+sinx

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Q: cracks between descending powers of x or a. Study the exa. Zx²-5xytyz wy – 3xy + y' sy +y 5. 280 + y…

A: Given that : 280+y+x+3y-2y+x. We will re-arrange the expression by taking the x terms and y terms…