Is the equation separable, linear, bernoulli, or homogenous? x4 + 4xy2 2x3 + x²y +y³ а. dx b. (e"cos(x))y' x4 + 6x²y³ C. y' = y + vx3 x + x2 cos() cOS

Q: Find the differential equation of (y cos x + 2xe^y )dx + (sin x + x²e^y) dy =0

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Q: Determine whether the differential equation is separable. y' (8x+y) c Cos O Separable Not separable

A: Given query is to find that differential equation is separable or not.

Q: The Bernoulli's form of the differential equation 2x³dy-− y(y² + 3x² ]dx = 0 is

A: As per our norms we have to write one question at a time kindly repost remaining questions.

Q: Find the differential dy of the given function. y = In√9-x² dy =

A: Given y=ln9-x2 Formula: ddx(ln u)=u'u where u is a function of x Now consider y=ln9-x2 The given…

Q: Verify that the function y = x sin(x) + x cos(x) is a solution to the differential equation: y" + y…

A: 1 have verified the differential equation by finding each derivatives

Q: Obtain the solution to the differential equation: cos*x- cos"y dx + cosxsin 2ydy = 0 a. cos*y(1+…

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Q: find a linear differential operator that annihilates the given function. y = x sin(3x)+ 3xe6x

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Q: Obtain a linear differential equation with real, constant coefficients that is satisfied 1 sin 2 1…

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Q: z = x siny + y sinx

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Q: 04- Determine the general solution of the following differential equat dy tan x. +у %3D sec х dx

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: Determine whether the differential equation is separable. y'= 4x cos (y)-xy Separable Not separable

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Q: Obtain the differential equation of the family of circles having their centers on the x-axis.…

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Q: 4. u = xz siny + yz cosx + xy tanz

A: Given,  u=xz sin y+yz cos x+xy tan z

Q: The solution of the differential equation using variable separable +8 sec y = 0 is da dy O siny = 8x…

A: Divide by secy and multiply by dx the get the variable separate

Q: A solutipn of the Ordinary Differential Equation x'y" - 2xy' + (x? + 2) y = 0, x > 0 is defined by…

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Q: Solve the differential equation by variation of parameters. y"+y = n²(x) xx) = c₂cos(x) + csin(x) +…

A: The solution is given as

Q: Show that y1 = sin x² and y2 = cos x² are linearly in- dependent functions, but that their Wronskian…

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Q: Find the general solution to the differential equatio y" + 4y = cos 2x (where y' = ) dx

A: When the right-hand side of a higher-order linear differential equation contains a function of the…

Q: For an exact equation, Show that this differential equation cos(x+ y)dx= (3y² +2y+ cos(x+ y))cdy = 0…

A: We  are given the differential equation : cos (x+y)dx+(3y2+2y+cos(x+y))dy=0 On comparing with :…

Q: At any particular time, the rate of change at which the vertical position of an object moving in…

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Q: Q19// Solve the partial differential equation du = Iny sin-x given that дхду = cosx when y-0 and u=y…

A: Initial value problem are those problem in partial differential equation in which initial condition…

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

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Q: The standard form of the differential equation cosx y' + cosx y = x sin x is: None of the above O…

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Q: Find the differential dy of the given function. y = In√√/9-x² dy =

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Q: Find the differential equation by eliminating the arbitrary constant/s. Gedr cos x + Cge y = c1e 3x…

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Q: (y') ² + (x-2x^-½) y'+ x^-1 - x^½= 0

A: As per the company rule, we are supposed to solve one problem. Therefore kindly repost the second…

Q: Show that a harmonic function u (x, y) satisfies the formal differential equa- = 0. azdz

A: Consider the provided question, Given, ux,y is harmonic function. We have to show that ∂2u∂z∂z¯=0.…

Q: Form the differential equation for the function x+2y=a sin3x-bcos3x

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Q: Find the differential equation of the family of circles with center at the origin. a+x y = .2 x'+1

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Q: Solve the Euler-Cauchy differential equation dy -3x + 4y = dx In?x - Inx

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Q: Find a linear homogeneous differential equation with constant coefficients so that the general…

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Q: Obtain the differential equation whose general solution is y= a sin 2x b cos 2x, where a and b are…

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Q: y" +y = cos x ; when x = = 0, y = 0,y' = 1 %3D

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Q: Find the differential equation of the family of parabolas with vertex ar Focus on the x-axis * O y =…

A: We have to find

Q: from the partial differential equation by eliminating the arbitrary function z (x² + y? + z?)

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Q: Find the solution of the differential equation y" + y' = sin x -sinx +cosx а. y = C1 + C2 e¬x SX b.…

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Q: Consider a differential equaUion -x2 y' = xy + xe

A: we have been given a differential equation with initial condition y(0)=0 y'=xy+xe-x2

Q: Verify by substitution that the family of functions y = -(x) sin(-3x) + cx is a solution of the…

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Q: Obtain the differential equation of the family of curves, parabolas with vertex and focus on the y…

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Q: Use Euler method to estimate the solution of 1 sin 5x - 5e cos 5.x, dx with initial condition v(0)=0…

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Q: What is the general solution to the differential equation (tan x)dy – (4y In y – y tan³x)sec²x dx =…

A: Given differential equation:(tanx)dy-(4ylny-ytan3x)sec2xdx=0To find: General solution of the…

Q: Solve the differential equation as follows: (6xy* – sin x tan y)dx + (12x²y³ + sec? y cos x – 5y²)dy…

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Q: Evaluate the curve f(x, y) = 0 which passes through the point (0,4) and satisfies the differential…

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Q: Solve the equation by the method o f homogeneous differential equatio ns y' = ² + tan (2) x In |tan…

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Q: Verify that the indicated function y = y(x) is an explicit solution of the given first-order…

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Q: Solve the differential equation by variation of parameters. y" + y = sec (0) tan(0) y(0) = C₁cos (0)…

A: Sol:- While solving the question , initial θ is considered as 't' At the end , we will replace t…

Q: Verify that the indicated function is an explicit solution of the given differential equation.…

A: We have to solve given problem:

Q: For the differential equation y' = 2y - x, draw line segments representing the slope field at the…

A: Given that, y' = 2y - x dy/dx = 2y - x At the point (1, 2) we get: dy/dx = 2(2) - 1 dy/dx = 4 - 1…

Q: What is the general solution to the differential equation (tan x)dy – (4y In y – y tan³x)sec²x dx =…

A: We will convert given differential equation into linear differential equation by appropriate…

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.