1.Solve the given problem W = f(x, y, z) = 3x²y+ yz² + 2z³ fxis equal to ? fyis equal to ? fzis equal to ?

Q: 2. Solve the boundary-value problem = 4, y(0,t) = y(5,t) = 0, y(x,0) = 0, y.(x,0) = 5 sin rx. %3D

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Q: Show that there is no solution to the boundary value problem y′′ + 4y = 0, y(0) = 0, y(pai) = 1.

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Q: Ⓒ Solve зик subject to + 2x x = 0 u(x,0) = in Rx [0,00) n(x)

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Q: 4. Find the solution of the following set of simultaneous equations by LT with conditions y(0) =…

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Q: Find the complete solution of dy + dz = 3z'ydz

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Q: Use the method of variation of parameters to find a particular solution of y" – 5y' + 4y = e*. %3!

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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: 3. General solution of (ylny - e-xy)dx + ( + xlny) dy = = 0

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Q: Let z=xIn(x²+y²-e)-235xy, x=te, y=est. If the value of oz when s=2 and t=1 is equal to Ae?+Be", then…

A: Here, the given functions are: z=x lnx2+y2-e4-235xy, x=t es, y=est so, z is a function of x and y…

Q: ck that y(x) = e rx with r satisfying ar 2

A: Introduction: Introduction: In mathematics, differentiation is the process of determining the…

Q: 4(a) Verify that the equation y = In(*/y) is an implicit solution of the IVP, %3D ydx (xy + x)dy…

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Q: What equation does the extremal y of the isoperimetric problem J(y) = S (2y² + y)dæ subject to the…

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Q: Q.5 Consider the Sturm-Liouville problem d -(xy')+(2-1)y=0, dx y'(1)=0, y'(e²)=0

A: Given,           xddxxy'+λ-1y=0,    y'(1)=0, y'(e2)=0.

Q: Solve the following Euler-Cauchy type equation: 1 (x² D² + 3xD+ 1)y = - 3xD+ 1)y = (1 – x)² ' d…

A: Given equation is, x2D2+3xD+1y=1(1-x)2 Take, (x2D2+3xD+1)y=0 Then assume, y=xn,…

Q: An equation that considers both the above assumptions is dP P kP(1 M - dt

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Q: compute the first three successive approximations to the solution of the ini- tial value problem dy…

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Q: 6 By Separation of variables, Solve the following 5 PDES :- d²4 d24 dx² 0 o u(e,t) = u(s, t) =6…

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Q: 2 1. The cissoids y : %D а —х

A: Given the equation  of cissoids y2=x3a-x As per our guideline we are supposed to answer only the…

Q: Determine the values of 12 for which the boundary value problem du + 2°u = 0, 0< x < 5, dx2 du (0) =…

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Q: x°y" – 3x'y"+ 6xy'– 6y = 0 -

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Q: Find the general solution to the DE using the method of Variation of Parameters 8 y" – 4y = e2x + 1

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Q: e the Cauchy problem y' = y cosx, y(0) = 1.

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Q: Qe/ Salve the Euler- Cauchy equation xy'- xy+9y=o ?

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Q: 5 By separation of variables, Solve the followin PDES :- du dt d2u dx2 @ o U (0₂t) =(4,t) = G u(x,0)…

A: Given is the Partial Differential equation ∂u∂t=2∂2u∂x2…

Q: Find general solution to Cauchy-Euler equation: (t^2)y''-2ty'-3y=t^2

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Q: Solve the given boundary-value problem. y'' − 2y' + 2y = 2x − 2,  y(0) = 0, y(π) = π

A: Find the homogeneous solution of the given IVP as follows.

Q: y" – 4y' + 8y = x², y(0) = 2, y'(0) = 4

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Q: x²y"+xy'-y= x 2

A: Given Cauchy-Euler equation is x2y''+xy'-y=x.

Q: b. Solve by using variable separation method. = 0 ax2' ay2 Which satisfies the conditions, u(0, y) =…

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Q: Now, we can set zy = 0, substitute 2x for y, and solve for x. + 21 = 0 = -21 X =

A: Substitution method: - The substitution technique could be a simple approach for determining linear…

Q: 2. Show that the substitution u = y' leads to a Bernoulli equation and solve this equation: xy" = y'…

A: See the attachment

Q: 2+ Problem 3/ Evaluate z*dz along the line y=

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Q: Variation of Parameters ex y" – 2y' + y =

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Q: a. Solve the initival value problem: y = 5 cos (2r)/(6+ 5y), y(0) = -1. -6+V36 - ( sin (x) + 10 2. A…

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

Q: 3. Find the general solution of the Bernoulli's Equation. y = 5.4y – 12y?, y(0) = 1.

A: the general form of the Bernoulli equation is dydx+P(x)y=Q(x)yn we have, y'=5.4y-12y2 rearranging it…

Q: #3. Solve the fallowing Caucly problem in R" x(0,0) U4-Ou t cu = 0 u =9 On IR"x{t =0}. where c is a…

A: Given the Cauchy problem as  ut-∆u+cu=0,       in ℝn×0,∞           (1) re-write the equation (1) in…

Q: Solve the following initial valuLe problem dy 2ry)/v- and y(0) . 半

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Q: Verify that the function y(r) = 2, is a solution of the initial value problem dy + 2y = 3y, v(0) =;…

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Q: Determine a particular solution of the following using the method of variation of parameter. TH…

A: Here we first find the auxiliary equation. Then we can find out the complementary function, in…

Q: Find the general solution of the di f ferential equation *+ x .2 d²y + (x² – )y = 0.

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Q: We wish to find the solution to dy = 26y that passes through the point (x, y) = (1, 3).

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Q: 2. Solve the following problem 10 (хи — 2x2 — 5и?)dt max | 0, dx = x + 3u, x(0) = 6, x(10) free dt

A: We will use Euler-Lagrange equation to solbe the optimization problem.

Q: 3. Find the general solutions of, dy_x+y dx х-у, а.

A: given differential equation is  dydx=x+yx-y

Q: If u(x, t) = E1 fn(t) sin(nx) is the solution Utt – 9uzz = 2e2t sin(3x) + e-2t sin(4x) m=1 u(0, t) :…

A: Given: ux,t=∑n=1∞fntsinnx is the solution of the PDE…

Q: . Solve the following problem (a) Y'(t) = XY(t) + 1, (b) Y'(t) = \Y(t)+t, Y(0) = 1. Y(0) = 3.

A: In this question, we will solve the given linear first order differential equations.

Q: Prove that eª (x – 1) = + +c is a solution to xy dx + (y+ 1)e¯ªdy = 0. 2y?

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Q: Solve the variational problem 8] +2y (x +y)] de = 0, given y (1) éy (2) 0. %3D

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Q: 3. Find the general solution of the Bernoulli's Equation. y = 5.4y – 12y, y(0) = 1. %3D

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Q: 16) Use the method of Variation of Parameters to solve 3y" – 6y' + 6y = e* sec x.

A: To find the solution of the below differential equation using the variation of parameters. 3y'' −6y'…