Solve the equation. List both the exact solution and its approximation rounded to tw exist, enter DNE.) 2 - 148x-2 = 0 %3D Exact solution: x = Approximate solution: x =

Q: dy 4x2-х-2 : У(1) %3D 1 dx (х+1)(у+1)

A: Explained below

Q: Find a solution to the euler equation, from : rx2 (2? – y/²)dx

A:

Q: ) Use the d'Alembert solution to solve = 2 -00 0, 1 u(x, 0) = e, u(x, 0) : 1+ x2*

A: As per our company guidline we are supposed to answer only first question. Kindly repost other…

Q: Solve the DE. If o(x) is the solution to the DE, find o( - 2) $( – y = xe- x*: (0) = 0

A: Solution of the differential equation

Q: 2) Determine the constant A such that the equation (x² + 12ry) dx – (Ar² + 8y) dy = 0 is exact and…

A: The differential equation P(x,y)dx+ Q(x,y)dy =0 is an exact equation if and only if…

Q: Solve the Bernoulli equations given below dy, y dx 2x %3D

A: Given:

Q: Obtain the solution of the dy 1 1.x- + y = dx dy y2

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: Solve this Di fferential equat ion by applying (Variation parameters) y+y%3DSE c x

A: The given differential equation is y''+y = sec x

Q: Subsitulion Solue The DE using subsitilan metorJ

A:

Q: Exercise: Apply V=mu and then (*y)=fcx)+ JCY) to solve the fellowing equation 2. 11

A: Given equation is, x2ux2+y2uy2=xyu2.....(1) And,  v=lnu....2vx,y=fx+gy.....3 Aolving equation (2) we…

Q: 12. (D² + D)y = -cosx %3D

A:

Q: * + ydx + (V.y + x)dy = 0 V x ; y = 4 when x = 1 х + уjdx +

A: Exact differential equation problem....

Q: Sc ot'(3y)dy

A:

Q: Solve an exact equation?  M(x,y) + N(x,y)*dy/dx = 0

A: Given: M(x,y)+N(x,y)(dydx)=0

Q: Solve the given Bernoulli equation by using this substitution. 1 ty' + 4ty - y³ = 0,t > 0

A:

Q: (1+ y²)dx + (x²y + y)dy = 0

A:

Q: y" + 2y' = 121?

A: To find the general solution of a given non homogeneous differential equation first we will find…

Q: 'ind the general solution and a particular solution by variation of param- y" + y = csc² (x)

A:

Q: 1. Obtain the general solution unless otherwise instructed d²y 1. y = 10sin²x dx2 %3D - SUMMARY OF…

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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: dz dw || Z-W z+w

A:

Q: Using the method of undetermined coefficients, write the form of the assumed particular solution for…

A: Given: y"+2y'+y=x2e-x Auxiliary equation are,  m2+2m+1=0 (m+1)2=0 m=-1,-1

Q: The appropriate form forVthe method of underenmined coeerents was used to solve the DE y" + 3y +…

A: c NOT option is correct.

Q: Without solving, classify the following equations as to: separable, homogeneous, exact, linear,…

A: Classification of the differential equation

Q: solve the equation by using Bernoulli's equations. y' + p(x)y = f(x) y ln y

A: Y’ +p(x)y =f(x)ylny divide equation with y both side we get y’ /y +p(x) = f(x) lny now consider lny…

Q: = P + csc- 10. %3D dx x х

A:

Q: The solution of DE.s divided into complementary solution and particular solution. * O True False

A: Consider a nth order differential equation dnydxn+dn-1ydxn-1+dn-2ydxn-2+.........................+y…

Q: Obtain the general solution unless otherwise instructed 1. arž -y = 10sin²x dx² SUMMARY OF ANSWERS…

A:

Q: y" + 2y' = 2te

A:

Q: Solve for the particular solution: dy = y + Vr2 – y?, y(2) = 0 %3D - da

A:

Q: 5. e²y$/1- e' dy

A: Solve the integration

Q: Solve the initial value problem. d?y = 6-30x, y'(0) = 8, and y(0) = 4 dx? %3D y(x) = |

A: According to question,Given differential equation,d2ydx2 = 6-30x,y'0 = 8y0 =4

Q: Appy Runge Kutta method to solve y' = 1+ y? ,y(0) = 0, Calculate the value of y %3D correct to 4…

A: Here we use the second order R-K method with step size h=0.2. the values of y at x=0, 0.2 , 0.4 are…

Q: Seve: dy %3D e A Be

A:

Q: Solve the equation with homogeneous coefficients. (3y² – x²)dx – 2xydy = 0

A:

Q: Q2/A/<he di fferential equation is yedx +3xay+dx +dyno diff erential when fineling the solution to a…

A: To find: The solution of differential equation y2dx+3x2y2dx+dy=0 and also find the constant (c) at a…

Q: 3x(xy – 2) dx + (x³ + 2y) dy = 0

A: Given differential equation is     3xxy-2dx+x3+2ydy=0

Q: dy %3D dx = (9x + 4y + 1)?

A: The given equation is, dydx=9x+4y+12                     .........1 Let 9x+4y+1=v…

Q: Question 1 Explain that (AB)" = BT AT 21 A = 0 1 3 402 1 and B = 2 0 -1 1 1 -2 1 3

A: Let's find.

Q: Solve the given DE using 3 methods/possible solutions: Attach your complete solutions & answers (2y3…

A:

Q: y dx + (3x – xy + 2) dy = 0 -

A: As per the instruction, we will be solving only the first one. For (4),We will solve it by Exact…

Q: y' = e2/y, y(0) = 1, 0 st< 2, h = 0.5 %3D

A:

Q: Qi) Solve the following PDES by direct integration. 2) = 0 дх ду 3) = x?y %3D дх ду dxdy azu -2t and…

A: Solve PDE by direct integration.  According to guidelines we solve only first question.

Q: Use the method of separation of variables to solve the heat conduction equ д?и 1 ди k > > 0

A:

Q: Solve the IVP. Show the steps of derivation, beginning with the general solution. 14. dr/dt = -2tr,…

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

Q: (ylny – e¯xy)dx + ( + xlny) dy = 0

A: Solution :-

Q: 10. Solve the equation for the exact solution. TC arccos y- 3 %3D 6.

A: Given, arccos(y-π/3)= π/6 Multiplying both sides by cos we have, (y-π/3)= cos(π/6)

Q: y™ -2y = 0 %3D

A: Given the differential equation y''''' - 2y'''' = 0. Auxiliary equation is m5 - 2m4 = 0

Q: • Find solutions using EXact Iquations 1.) solve lysinx t xycosx) dx + (xsinx +1 )dy=D0 tind the…

A:

Q: test for the exactness and solve the IVP, critically outlinethe particular solution. (x + 5exy)dx…

A: Given differential equation is x+5exydx-exdy=0, y0=-2