use the Lagrangian method to solve:   U=(x+3)(y+5) given 30=3x+2y

Q: Q2. Solve the Bernoulli IVP, 1 x²y/ – 2xy = 3y*, y(1) = 2°

A: Solution of the differential equation

Q: Q2. Solve the Bernoulli IVP, x²y – 2xy = 3y*, y(1)

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Q: solve using the appropriate method. (y − 1)y'= t , y(1) = −3

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Q: Solve x?y" – 2ry' + 2y = x³ In x by first finding the complementary solution and then using the…

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Q: Find the solution. 2y" - 3y' + y = 0 (A By = c,e 1- ©y = c,e Dy =c,e

A: Find roots of  characteristic  equation  of given differential equation .If roots are real and…

Q: Find the particular solution of (y + Vx² + y²)dx – xdy; when x = v3, y = 1

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Q: Use separation of variables to find an explicit solution. xyy' = 2xy + y?

A: Idea: after separating x,dx and y, dy terms together. we take integration on both sides . after…

Q: (x² + 4xy + 2y²)dy + xydx = 0

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Q: Find the solution by using Solution of 2nd order D-Es 2 X ý XỨ ty - xy + y = Lnx -

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Q: dy - y = e2*y³ dx

A: Let's Solve,

Q: Use separation of variables to find an explicit solution. xyy' = 2xy² + y² %3D

A: Follow the steps below to solve a differential equation by the variable separation method. First,…

Q: solve the DE y'' - 5y' + 6y = 32xe2x, y(0) = 1, y'(0) = 0

A: *Concept:- the give differential equation is Linear differential equation of higher order with…

Q: Use the separation of variables method to solve 4urz = Utt, H 00 ur (2, t) = 0 ur (0, t) = u(x,0) =…

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Q: t with y(0) Solve y + 5y ing %3D 4 express- the particular solution as a convolution.

A: In this question, we have to find the particular solution of the differential equation by help of…

Q: use Separation of Variables to find the general solution. yy' = x

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Q: Q8. Solve the non-homogeneous Cauchy-Euler equation (a) x?y" – 2y = 3x².

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Q: Find the particular solution of -4y = 3x – 1 given that when x=0, y=0 and d2x dx dx II

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Q: (r²+y + y³) dx – x dy=0

A: →∫1a2 + x2dx  = 1atan-1xa→ddxuv = udvdx + vdudx

Q: Solve the DE using the method of variation of parameters: x²y" – 4xy' + 6y =30x³, y(1) =5 , y’(1) =5

A: homogeneous system is  compare this equation with  so here we have

Q: B. In each exercise, obtain the particular of solution. 2. y(9x - 2y) dx - x(6x – y) dy = 0; when x…

A: Differential equations

Q: Use 4t order Runge-Kutta Method to solve dy = y' = x+y, y (0) = 1 & Y(2) = ? Use h = 0.5

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Q: Using the variation of parameters, find the particular solution of (D2 +1)y = secx

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Q: Conside the DE y" + a²y = 0; y(T/2a) = 0, y'(1 /2a) = -a where a is a constant. Solve it by using…

A: We are given the DE,                  . where a is constant.  First, we will solve by using trial…

Q: Solve y′ = t − 5ty using both separable and linear methods, and verify that your answers are the…

A: Given data:   The given differential equation is: y’=t-5ty.     The given differential equation can…

Q: G) (2x-yJdx + (4x. +y-3)dy=

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Q: Determine the type of DE/method of solution to be used and solve. y′ = x3 − 2xy, when x = 1 and y =…

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Q: Check that y Cx) = e* is the Solution of y" + y' - 2y = 0

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Q: Use the method of variation of parameters to solve y" – 4y +4y = 2e". %3D -

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Q: Find the general solution using the method of undetermined coefficients. dx +7x=8e° dt -41

A: Answer

Q: Find the general solution using variation of parameters. - 4y + 4y = (x + 1)e²-

A: To solve the following problem

Q: Use the separation of variables method to solve 4UTr H Utt: 00 uz (0, t) = uz (2, t) = 0 u(x,0) = x,…

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Q: Use Newton-Raphson method to solve the system x* + y – 1 = 0 y* – x +1 = 0 with the starting value…

A: We will use the following Newton-Rapson formula for finding the roots of 2 variable equations.…

Q: Determine the type of DE/method of solution to be used and solve. y(y3 − x)dx + x(y3 + x)dy = 0

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Q: Use variation of parameters to solve the general solution 1 (D² – 3D + 2)y 1+ e¬*

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Q: By making the change of variables u = 2, v = x, find the general solution of yfyy +fyx + fy = 1.

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Q: - y" – 2y' + 1 = (x + 1)e2x

A: Just I have used the method of variation of parameters and easily find the required solution.Final…

Q: 2d) Let a e R find the solution of y' (x) – ay(x) = 0

A: as you didn't mention question number to be solvedso I solved first question. For Further solution…

Q: dy Find the general solution of xy + y² dr x2

A: According to our guideline, we can solve only first question of multiple question.So, here we solve…

Q: Use Gaussian Eleminetion to solve 20+ y + 2Z =8 3y + 3Z a-4 4¢ + 24 - Z = Iv

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Q: (D³ + 2D² − 5D − 8)y = 0, when x = 0, y = 0, y' = 0, y = 2 - -

A: Given  (D3+2D2-5D-8)y=0 and when x=0, y=0, y'=0, y''=2. The formula for differentiation is…

Q: x''-4x'+3x=(e^t)/(1+e^t) Using Variation of Parameters method, find the general solution.

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Q: If y(t) is the solution of - 2y = 4, y(0) =1, then y(t)= %3D %3D

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Q: Use separation of variables to find an explicit solution. xyy' = 2xy 2 2 + y?

A: using seperation of variables  and then integrate....

Q: Solve using the method of variation of parameters y" + 3y' + 2y =: 1+ e*

A: Given that: y''+3y'+2y=11+ex

Q: 1. y' = x3 – 2xy, when x = 1 and y = 1

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Q: Use variation of parameters d²y +pdty+94=Fx) plem) to find a particular solution to y" – 2y - 15y =…

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Q: Solve the DE by Variation of Parameters (D³ + D² – 2D) y (0) = 0.4, y' (0) = –0.4, y" (0) = -0.4

A: The Symbolic form of the equation is D3+D2-2Dy  =4e-2xcos x Auxiliary  equation is D3+D2-2D=0…

Q: Solve for the general solution. d³x dx -7. - + 6x = 0 dt3 dt

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Q: Use the separation of variables method to solve 4urz = Utt, H 00 ur (0, t) = ur (2, t) = 0 u(x,0) =…

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