dx dt -x + y + 2et ip dt — у — е-t

Q: the solution for the I.V.P. dy -y-Y dx y(0) = 1 is Select one: O a.

A: Here we have, dydx=y3-y,   y(0)=1

Q: Solve the D.Eusing Variable Separable Method e*(y? + 1) dx = 2y(e*+4)dy %3D Paragraph BIEE

A: Answer and explanation is given below..

Q: Find the constant a so that exy + y = x - 1 is an implicit solution to dx A. B.-2 C. -1 D. 1 3 E.…

A: Given exy + y = x - 1 is a solution of given differential equation.

Q: Exercise 3. compare the values of dy and Ay in each case (3a) y = 0.5r" I = 2 Ar = dr = 0.1 (3b) y =…

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Q: Solve the homogeneous equations (x + y) dy + (x - y) dx =0

A: Given,

Q: 4. Find an implicit solution using the substitution u= or y3ux dy dx x+xy %3D

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Q: 1. Solve by D operator method d?y dy -2y +y x2e3% dx2 dx Solvo hu

A:

Q: what is the annihilator for y=x e*cos 2x A D²-2D+5 B (D²-2D+5)² © D?+5 O (D²+5)²

A: We are asked to find the annihilator of the function.

Q: Find the solution of the second order homogeneous linear equation when d2y/dx2-4 dy/dx - 4y = y ; y…

A: Given differential equation is d2y/dx2-4 dy/dx - 4y = y ; y (0)=1 ,y'(0)=2

Q: HW/ solve the simultaneous D.Es. using L.T. y'+z =t, z'+4y = 0, y(0) = 1, z(0) =-I,

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Q: H.W: show that the equations are homogeneous and solve: 20 2. x² dy + (y² - xy)dx = 0

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

A: We need to evaluate integral.

Q: Find an integrating factor and solve the equations (i) (3x2y + 2xy + y2) dx + (x2 + y2) dy = 0…

A:

Q: Solve the order linear equation, dy dy 1 +-y=x, y(1) =5 dx x + p(x)y=r(x) dx x 14 + Solution: y= 3…

A: The initial condition in an initial value problem is used to determine the integration constant that…

Q: The general solution to d?y/dt2 = 25y is

A:

Q: What is the annihilator for y=x e*cos 2x ? (D²+5)2 ® D² +5 © (D²-2D+5)2 D D2-2D+5

A: See the solution.

Q: 3 – 6xy – 2y) dy = 0 ху Find the general solution of (ye - 2y) dx + (xe А. eу + 2хy3 - у? %3D с В.…

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Q: y? x² 4 Find dV , where E is the solid y2 x2 + 4 z2 - <1. 9 + +

A: First we have Choose suitable parameters.

Q: Þ(x) = x² is an explicit solution to dy 2y dx ylgn ihi

A:

Q: (x² + y²)dx – xy dy = 0

A:

Q: Determine the value(s) of r such that y (t) = e"t is a solution to y" + y' – 6y = 0.

A: Since part B and PART C are independent of PART A question.  As per the guidelines I am answering…

Q: TEST IF THE GIVEN D.E IS HOMOGENEOUS. IF YES, SOLVE FOR ITS GENERAL SOLUTION. IF NO, PROCEED TO THE…

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Q: Find the general solution of (ye – 2y³) dx+ (xe А. еxу + 2хy3 - у? %3D С В. е — 2ху3 - у? %3D с 6xy2…

A: We have to solve the problem

Q: State whether the equation is ordinary or partial, linear or nonlinear and determine its order and…

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Q: Find the solution. d3x d?x dx – 2–=0 dt + dt3 di2 -21 ® y = c,+c,e'+c,e- -31 D y = c,++ce+c,e-2

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Q: Solve x'y" - 3xy' +4y = 0; y(1) = 5; y'(1)= 3 Using y=x" Aux Equation yc= C, XM, + CaX"a m2 or yc L>…

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Q: Q4: Find the general solution of d?y dy - 3 - 4y 3e2t + 2sin t - 8et cos 2t, dt dy y(0) = 2, (0) %3…

A: Given that  The differential equation  To find the general solution

Q: [dz dx (x+y+z)dy (c) CS imscarner

A:

Q: dy Find a solution of x dx = y². - y that passes through the indicated points. (a) (0, 1) y = (b)…

A: First we'll solve differential equation then put intial conditions

Q: (2х — Зу)dx + (2у - 3х)dy %3D0

A:

Q: Solve the Bernoulli equation dy + xy = xy³ d.x .A = (ce + 1)-2 .B y = (ce – 1)- .C y = (ce" + 1)-½…

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Q: y" (E) + 2y, Ct) -4y, Ct)= 0 C)+y, (t) -3y, CE) = 2 Solve using the resoluh'on by eliminah'on

A: For the solution follow the next steps.

Q: Find the general solution of the given second-order differenttial equation y" + 18y' + 81y =0 y(x) =…

A: we have to find the general solution of the given differential equation. y"+18y'+81y=0

Q: Q5: Find the general solution of d²y + 4y = 3 cos 2t, y(0) = 2, (0) = 1. dt %3D %3D dt2

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Q: H.W: show that the equations are homogeneous and solve: 1. (x+y)dy + (x - y)dx=0

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Q: Find the general solution of the DE x(y? + x)dy - y(y?- x²)dx% = 0. %3D (x-y) In x +y In y =cx + y O…

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Q: Solve the equation (y+ u)Ux+yuy = x -y with the initial conditions u(x, 1) = 1+ x. %3D

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Q: Solve the homogeneous equations (x2 + y2) dx + xy dy = 0

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Q: What is the annihilator for y=x e*cos 2x ? A (D2-2D+5)2 B (D2+5)2 © D2-2D+5 (D D2 +5

A: A detailed solution is given below.

Q: Find the DE whose general solution is y = Ae Bx A. yy" - (y')2 = 0 B. yy" + (y')2 = 0 C. yy"- y' = 0…

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Q: (x+?y=4)dx - (2x +y-5) dy = %3D (コメ13yー1)dx + (2x+3y+3)<y

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Q: Let y = 0, +aqt+azt? +az13+aq +agt5+ag!6+ +а.t+ be the solution of d?y. +taY +y=tan-t ; y(0)=1,…

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Q: * y"-2xy'+uy = 2, yto)=0, yl)=1 =)ytx)=? %3D find the solution using numerical solution

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Q: 2) Obtain a particular solution for d*y d?y dy + +y = x³ + 2x +1 dx4

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Q: 3. Find the complete solution of (x²y+y³ – y)dx + (x³ + xy? + x)dy = 0 Hint: Expand and Simplify

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Q: Using separation of variables, find a solution to the equation dy = -5t*y subject to the initial…

A: Please refer the attached image for complete solution.

Q: Consider the second order DE 2y" + 3y' + y = 0. Find two different solutions y1 and y2 of the form y…

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Q: What is the annihilator for y=x e*cos 2x? A (D2+5)2 B D2+5 D2-2D+5 D (D²-2D+5)2

A: Explanation of the answer is as follows