Use Euler's explicit method to solve the ODE dy/dx = 2.3y + 4e^−0.2x from x = 0 to x = 3 with the initial condition y = 4 at x = 0. Use h = 1.5 .

Q: dy/dx if y=tan((1-2x)/(1+x)) dy/dx if y=x^4 ln(3x-1)

A: 1)    y=tan1-2x1+x2)    y=x4ln(3x-1) Hint:  Chain rule and then uv and u/v rule of differentiation

Q: Show that given differential equation dy y cos x + sin y + 9 – 0 is Exact and dx sin x + x cos y + x…

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Q: use appropriate substitution to solve differential equatio dy/dx-(2/x)y=-x^2y^3

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Q: and dr= %3D Solve for the differential of y When y=sinxx x

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Q: sec( c)+y dy e sec do

A: Given differential equation is homogeneous equation

Q: on) solve the Differential en by using vanation of parameters - 24 (+12 yll -24¹ +y₁

A: Please see the below picture for detailed solution.

Q: find a particular solution yp of the given equation. primes denote derivatives with respect to x.…

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Q: 31+2 dy - of the function y= dt 7. Find +4 dy of the function y = 5 tan (6x)+ log, (36x² + dx 8.…

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Q: (2y-1 + cos 3z) 분. 4x3 + 3y sin 3x = 0 (1)

A: We know that if - M(dy/dx)+N=0 Then M(dy/dx)= -N Therefore- dy/dx= -(N/M)

Q: 3. find dy/dx of y= sinh 2x

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Q: Use the initial condition to find the particular solution of the differential equation. dy = 4xy…

A: In the given question apply the variable separable method, i.e, isolate the y terms on the left side…

Q: Solve the differential equation using Laplace transform of y"+y=6sin2t ; when y(0)=3 and y'(0)=1

A: The given differential equation is…

Q: (b) To determine To compute: The differential equaiton + x = sin 4t with initial condition x (1₁) =…

A: Given differential equation is: d2xdt2+x=sin4t . . . (1)The initial condition is: xt1=0 And…

Q: Verify that y=sinx is a solution to dx dy 2cos x-sin x+y and solve the 2 cosx differential equation…

A: Given Information :  Differential equation : dydx = 2cos2x - sin2x + y22 cosx  y1 = sinx y(0) = -1

Q: Make the Non exact differential equation xy dx+(3y^2+2x^2−20) dy=0 to an exact differential…

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Q: The differential equation of the form = sin x has a degree equal to dy %3D Enter your answer as a dr…

A: We have to find out degree

Q: show Itat the differential equation メり dy - -2-ye" dx xーとリ Xe 29 its exact and find its Folution

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Q: Determine the equation of the curve passing through the origin in the from y = f(x) which satisfies…

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Q: (3 şiny-5x) dx + 2x²cotydy = 0 hint: let 2 =sinu

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Q: Solve for the DE: (y²-1)dx + (2xy- Siny) dy =0 When x= -1 ; y= 0

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Q: SOLVE FOR EXACT DE DIFFERENTIAL EQUATION хdy — ydx 4. | = x³ dx y2

A: Given that: xdy-ydxy2=x3dx

Q: Solve the differential equation by variation of parameters. y" + y = sec (0) tan(0) y(0) = c₁cos (0)…

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Q: Find the general solution of the differential equation and check the result by differentiation.…

A: Given the differential equation:

Q: Solve for the differential of y when y= sinzx. x= -, and dx 3 2 4

A: we have to solve the problem

Q: Solve the initial value DE y' - ytanx = sinx, y(0) = 1 5-cos 2x 5-cos 3x 5-c A) y B) y = с) у %3D 4…

A: Given differential equation is y'-ytanx=sinx,   y0=1 Compare the given differential equation with…

Q: Compute dy/dx for the function. 5) y = In sinh 6x

A: topic- derivative of a function

Q: 15. x" + x = tan t; x=-(cost) In(sect + tant)

A: Given, x''+x=tant x=-costlnsec(t)+tan(t)x''=cos(t) ln(tan(t)+sec(t))+tan(t)

Q: Consider the differential equation dy dx with a particular solution y = f(x) having an initial…

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Q: solve for the differential eq   (8x−10xy+4y^2sin^2 (x) )dx=(2ysin2x+5x^2−4xy)dy

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Q: Explain why the initial Value problem dy/dx=x-cos(y); y(1)=pi has a unique solution. For that…

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Q: Solve the separable differential equation. dy (1+y²) coshx dx 9+sinh x

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Q: If y = (1/2x)(sin(lnx)-cos(lnx)), find dy/dx.

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Q: dy = ky| 1- dx L)

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Q: Show that the sine integral satisfiesthe (differential) equation xS'(x) + 2S''(x) + xS'''(x) = 0.

A: Given information: Sx=∫0xsinttdt To prove xS'x+2S"x+xS'''x=0

Q: у" + 16у — 0; Уi — сos 4x

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Q: (f). Verify if the differential equation given by 10x°y* + e¬Y + 3 sin(4x + 3y))y' + (6x²y° + 4…

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Q: A population x of rats satisfies the DE dx /dt ka?. Initially there are x(0) = 2 rats, and their…

A: The general solution of a differential equation always contains a constant of integration. The…

Q: Solve for first odrer differential equation    (x^2+cosy)dy+(3x^2+2xy)dx=0 where; x=0 , y=π/2

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Q: 4te dt TOT

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Q: Find the function y: (0.x) → R that satisfies the ordinary differential equation ry'(x) + y(x) = x²…

A: Given : y : 0 , ∞→ℝ   ;  xy'(x)+y(x)=x2 cosx        ;  yπ = 0 To Find : solution of ordinary…

Q: dy Solve the differential equation dx + y + x y with initial condition v(0) =-1 and 03x32 with step…

A: The given differential equation is, dydx=x2+y+xyy'=x2+y+xy The initial condition is y0=-1 So, x0=0…

Q: (2х — 5у + 3)dxх — (2х + 4у — 6)dy %3D 0 - -

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Q: The differential equation (3ycosx+ 4xe* + 2x²e* ]dx + 3(sin x + 1 )dy = 0 is exact because ƏM ƏN

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Q: Use integration to find a general solution of the differential equation                dy/dx = sin…

A: given differential equation as dydx= sin 2x or it can be written as dy=sin 2x dx

Q: tan(2x + 2). Find the differential dy when x = Let y : 4 and dx 0.2 Find the differential dy when x…

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Q: Since dv = cos( x) dx, integrate the differential equation to obtain the function v. =D A dv Cos( x)…

A: Since dv=cos8xdx, the first missing term is 8. Substitute cos8xdx for dv in ∫dv to obtain ∫cos8xdx.…

Q: Is the differential equation y sin 4x dx + x cos 9y dy = 0 exact? %3D Choose the most appropriate…

A: A Diffrentaial equation in the form :-  M( x, y)dx + N(x, y) dy = 0 is an exact  if,   ∂M/∂y =…