exdct UUL OLLE factor. Then solve the equation. 16/ 2xy3 + x(1 + y² )y' = 0, H(x, y) = 1/xy³ %3D sin y ( cos y + 3e cos x + 17 3e-X sin x

Q: Q/ Find the generd solution of the differentiol equation y"+3y'=2sin(x)+cos (x) %D

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Q: Q5: Solve by using Modified Euler's Method. dy = x + cos(y) ;0 <x<1 ;y(0) = 1;h = 0.5 dx

A: Given the DE is dydx=x+cosy,0≤x≤1,y0=1,h=0.5. The modified Euelr's method is defined as follows:…

Q: Q1) Solve 1 + cos y – 2xy) dx – (xsin y + x²)dy = 0 +1

A: Given differential equation is  1x2+1+cosy-2xydx-xsiny+x2dy=0 This equation can be written as…

Q: 3.S dx C. ez? D. ex А. х В.-х? cos x 4. S9 dx V1+sin x A. V1+sinx B. cosx C. sinx D. 1+ sinx

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Q: Q5: Solve by using Modified Euler's Method. dy = x + cos(y) ; 0 < x <1 ;y(0) = 1 ; h = 0.5 dx

A: Disclaimer: We use the modified Euler's method to solve a first-order ODE and find the value of the…

Q: Solve the DE * 1-y² dx= (9+x*) dy=0 In (9+x*) – 4x² sin -1 y=C (B In (9+x*) – 4 sinly=C © tan…

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Q: Find the values of α and β that make dF(x,y) = ((1 / ((x^2) + 2)) + (α / y))dx + ((xy^β) + 1)dy an…

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Q: y" + 2y' = 2 – 5 cos(x), y(0) = 0, y' (0) = 1. %3D

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Q: dy +xsin 2y = x cos² y. dx Solve the Bernoulli equation.

A: Given: y' + xsin2y = x3cos2y ⇒y' + 2xsinycosy = x3cos2y ⇒y'sec2y + 2xtany = x3 Now, let tany = v ⇒…

Q: Check the DE if it is exact or not then solve it. (If it is not exact use the method by using…

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Q: x2-y2 dy 8. dx du Y: Formula: J Ta?-u² = sin-1 u V a

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Q: + Use Separation of variables to solve eくX<| Us co,t)こ0 I4 pts] ULx,0) = X

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Q: C. Find the general solution of the given variable separable equation. 1. 2cosx cosy dx - 3Isin x…

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Q: d'y Find for dr? y = 5x? cos(x) + 13 sin(x) d?y dz? ||

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Q: olve the following initial value problem using variation of parameters: y" + 4y = cos 3x y(0) = 0,…

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Q: (cos 2y – 3x?y?)dx + (cos 2y – 2x sin 2y – 2x³y)dy = 0 What is the general solution?

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Q: ve the tollowing differential equations: sin*x cos ydx + cos 2xdy%3D0

A: We are authorized to solve only one question, please repost remaining questions Differential…

Q: *10. cos Z = 0.5234 YX _ y 24

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Q: Q7// find the general solution 1 (sin-ix + =y)dx + sec-1xdy = 0 xVx² – 1

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Q: 1. Solve the given the equation using the integrating factors found by inspection. ydx + (x + x³…

A: Given that ydx+x+x3y2dy=0Solution :ydx+x1+x2y2dy=0this diffrancial equation in the…

Q: (y? cos x – 3x?y – 2x) dx + (2y sin x- x'+ In y) dy = o

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Q: (r+ 3r sin y)dr + (r* cos y)dy = 0 solve the differential equatio

A: solution :                 The given differential equatiy is            (x+3x3siny) dx+ (xy cosy) dy…

Q: Anjuer +2y°x ]dx+(2yx² – cos y)dy = 0, y(1)=n 3. n = Inx+x*y² – sin y #4 3. Solve

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Q: Q7// find the general solution (sin-1x + 1 y)dx + sec-1xdy = 0 1 xVx² – |

A: The detailed solution is as follows below:

Q: Advanced Math dy/dx=sin(x)+1 using euler method h=0.01 y(0)=1 y(1)=?

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Q: Find the solution. dy sin x x-+2y +2y = y (2) = 1 dx (A) y = (4 + sin 2 + cosx?) /x2 B в су %3D (3 —…

A: Given differential equation  xdydx+2y=sin xx,   y2=1 Linear differential equation with initial…

Q: و - هاد -3 10) dy dx 1 x cos y

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Q: Find the general solution of y(4) + y" = 3t2 + 4 sin t – 2 cos t

A: Given differential equation is y(4) + y" = 3t2 + 4sin(t) - 2cos(t)

Q: Solve the given higher order DE y" – y" + 3Dy – 5y = e*Sin 2x

A: Auxiliary equation corresponding to given differential equation: m3-m2+3m-5=0 Roots of polynomial…

Q: Determine ?? using undetermined coefficients: 1. y'' + y' + y = 2xex

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Q: IV. y-y=sin x+cos 2x +e

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Q: Find the solution. dy X-+ 2y = dx sin x y(2) = 1 A cy = (3 – cos 2x – tanx)/x? B x = (2 + cor2 –…

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Q: Test the equation for exactness and if separable: (2xy + 2x) dx = y dy

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Q: Solve by finding an I.F 1. xdy – ydx = (x² + y² }£x y - sin x 2. dy + -dx = 0 ......

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

Q: Find constants A and B such that yp(x) = A sin x + B cos x is a solution of dy/dx + y = 2 sin x.

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Q: 13. 2xy dx + y“dy= 0; y(0) = 1. Answer: [2r² + y² = 1]

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Q: Q) Find the general solution. dy sin-1x Iny dx II

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Q: Q4: Find the value of integral 1 1 1. 1+x4 1 V1–x²dx 1 cos(x + 1) dx 2. 3.

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Q: 3 sin y 2. Find the particular solution of xsin² y cos yy' +. 1+ ln x =4 ¡y(e) = 1/

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Q: Check for exactness and obtain the general solution. 1. (2xy – tany)dx + (x2 – xsec?y)dy = 0

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Q: Use the method of characteristics to solve the first order equation Ug – 2uy = 3 with u(x, x) =…

A: Method of Characteristics and General Solutions: The general solution of the quasi-linear equation…

Q: Solve the given problem below: (2x + y cos x) dx +sinx dy=0

A: We will solve it by exact differential equations method.

Q: ind general solution by separating the v y3 = (y* + 1) cos x %3D dx.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: evaluate the triple iterated integral.

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Q: The function y = 4e3x sin x is a solution of dy Зу + 4е3х dx COS X %3! (A) True (в) False

A: Differentiate y with respect to x

Q: Q8// find the general solution (tan-'x + (cotx)y)dx + (lnsinx)dy = 0

A: The differential equation is given as (tan-1x+(cotx)y)dx+(ln sinx)dy=0 Compare it with Mdx+Ndy=0…

Q: Solve the given DE: (yexy + cosx)dx + (xe*y)dy = 0.

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Q: Q1: Solve by using Euler's Method. dy = x + cos(y) : 0sxs1 :y(0) =1;h 0.5 dx

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

Q: Q1: Find general solution of D.E. cosh (x) + sinh(x) y = e* dx

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Q: [2x + y cos (xy)] dx + x cos (xy) dy = 0 solve for the particular solution using x = 1, y = 1/2 %3D

A: we have to solve the differential equation

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.