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Q: Find an integrating factor for the equation -20p° dp + – 15pqª dq = 0 and transform it into an exact…

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Q: Find the general solution to the given Euler equation. Assume x > 0 x2y" + 3xy' + y = 0

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Q: Find the singular solution to the Clairaut equation y = xy' + In(- 19 -y').

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Q: Consider the Cauchy-Euler equation a²y" – 9xy' + 25y = x + x° In(x), x> 0. Solve the equation by…

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Q: Find the general solution to the given Euler equation. Assume x > 0 x2y" - xy' + 5y = 0

A: Given differential equation ,x2 y''-xy'+5y=0

Q: the solution of the homogenous equation (хусот х -)dy - Ydx = o

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Q: find the solution to the Cauchy-Euler equation on the interval (0,∞). In each case,m and k are…

A: Since we have to find the Cauchy-Euler equation, we will substitute y=xm which will yield…

Q: 5. Show that 1 T = VI? + y? satisfies the equation Tz + Tyy = T3

A: Given T(x,y)=1x2+y2

Q: 4. (D² + 2D + 5)y = 4e-*cos²x

A: Given differential equation is: d2ydx2+2dydx+5y=4e-xcos2x Auxiliary equation corresponding to given…

Q: x°y"+ 2x?y"+ xy'- y=0

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Q: Determine the general solution of the second order "Euler equation" and specify the interval in…

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Q: Find the first approximation to the root of the equation xlog r-0.8 0using Regular-Falsi method…

A: The false position method or the Regula-Falsi method uses the formula below to perform the…

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

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Q: Use the explicit Euler method to plot the  estimate y(2) if y(t) is the solution to y' = t - y3 with…

A: Given IVP is y'=t-y3, y(0)=1 we have  f(t,y)=t-y3 Here using n=10 steps, Then step size h=upper…

Q: Use the method of undetermined coefficients to find the general solution: y" + 4y : = cos 2t

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Q: 5. Solve the 2nd- order differentinl equation: d'y dy dr +2 +y=e24 CS Scanned with CamScanner

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Q: 2²y" - 4.xy+6y= 0, y(2)=0, y'(2) = 4 %3D

A: The differential equation is given as x2y''-4xy'+6y=0x2D2y-4xDy+6y=0x2D2-4xD+6y=0 It is a Cauchy…

Q: find the general solution to the given Euler equation.Assume x > 0 throughout. x2y'' + xy' - y =…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find the general solution of the given differiental equation using the undetermined coefficients…

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Q: 2 11 3. x*y" – 5xy'+9y= 2x

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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: Show that a riccati equation with constant coefficients y'+ ay² + by + c = 0 has a solution of the…

A: To show that  a riccati equation with constant coefficients y'+ ay² + by + c = 0 has a solution of…

Q: Find the general solution of the Euler equation on (0, oo) x²y" 3xy' + 13y = 0 y(z) = Note: Use A…

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Q: 2. Solve the diophantine equation x = y'.

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Q: Transform to normal form and solve (showing the details!) 41. uzz + 2uzy + Uyy = 0

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Q: Show that the equation Əy + 2k Əx? possesses solutions of the form 00 2 c, e-kt 1" =0 Σ cos (a, x +…

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Q: Solve the @iven dif frerenticul equation uning the variables method of seperatio n of dy 4y+3

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Q: he equation ay"+ by' + cy = 0 has a unique solution satisfying y(0) = 1 and y'(1) = 2.

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Q: y" + y = 0, y'(0) = 0, y' = 2

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Q: Find the general solution to the given Euler equation. Assume x > 0 9x2y" + 15xy' + y = 0

A: Solution:- The given differential equation is  9x2y''+15xy'+y=0..........(1)

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A: We are given the following differential equation: 1+exydx+exy1-xydy=0 We have to find the general…

Q: What value(s) of k in the equation y = ekx will satisfy the equation y + y' = y"?

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Q: 7. Solve the Bernoulli Equation r +y² = ry dr

A: The Bernoulli equation is x2dydx+y2=xy. Calculate the value of y.

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

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Q: Solve the given second order differnetial equation using variation of parameteres: y'' -4y =xex

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Q: Find the general solution of the Euler equation on (0, oo) x'y''-7xy' + 32y = |

A: We need to solve the differential equation x2y"-7xy'+32y=0

Q: Consider the Cauchy-Euler equation x²y"-9ry + 25y = r+ r In(r), r>0. Solve the equation by first…

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Q: A stone, projected vertically upward with initial velocity 112 ft/sec, moves according to 8 = 112t -…

A: We have to choose correct option

Q: Find the first approximation to the root of the equation x - 2x- 5 = 0using Regular-Falsi method…

A: Intermediate value property: Let f(x) be continuous function in a,band if f(a)&gt;0, f(b)&lt;0 then…

Q: 46. y" +y = Itsin z

A: Consider the given differential equation: Here the objective is to find the solution of a given…

Q: Using the method of undetermined coefficients, what is the form of the trial particular solution y,…

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Q: Solve for the Bernoulli's equation -- ses 2ds = 5t³s3 .33 %3D dt

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Q: 3x?y" + 2xy' = 05 21"

A: Differential equation

Q: Use the method of Variation of Parameters to solve the following DE: у" — у %3D2х2 —х— 3.

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Q: Using the method of undetermined coefficients, what is the form of the trial particular solution y,…

A: We will find out the required value.

Q: Find all solutions of the equation in the interval 0, 2n). V3 cot0-1=0

A: To solve:  3cotθ-1 = 0

Q: Which is the solution to the equation 7n 37 2sin22x + 3sin2x + 1 = 0, x = 6

A: 2sin22x+3sin2x+1=0 Put x=7π6 in the given equation, we get…

Q: a. Find the solution to the heat equation

A: Given,            ∂u∂t=16∂2u∂x2,                t≥0,   0≤x≤5                   ...(1) u(0, t)=u(5,…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.