Find a first order differential equation for which y2 sin(xy) + (2xe)cos(x)) = 3 is an implicit general solution.

Q: Verify that the given function y = sin (x2 + C ) is a solution of the given differential equation:…

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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: y(x) = C₁ + C₂e²x cos(5x) + c3e²* sin(5x)

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Q: Determine whether or not y=C1 cos (2t) + C2 sin (2t) is the solution to the differential equation…

A: we check y=c1 cos(2t)+c2sin92t) is the solution to the differential equation y''+4y=0

Q: Determine the solution of the 1st Ordered Differential Equation: (x - y)(4x + y)dx + x(5x - y)dy = 0

A: We have to solve given problem:

Q: 1) Verify that the indicated function y = −(cos x) ln(secx + tanx) is an explicit solution of the…

A: First we will find y" Then put value of y" and y in   y"+y = tanx If we get  LHS =RHS then it means…

Q: у" + 25у %3D 5 tan? (5x) сos(5x) 2.

A: Given the DE is y''+25y=5tan25xcos5x. To solve this DE use the variation of parameters method.

Q: dy +(cos x)y = sin²(x) using first order linear differential equation. dx Solve (sin x) %3D

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Q: consider the differential equation dy/dx=sin(x)/y for which the solution is y=f(x). Let f(0) = 1…

A: Given dydx=sinxy, y0=1. By variables separation,  y dy=sinx dx Integrating on both sides,

Q: y' + (2 tan x)y = - cos'x

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Q: Solve using the non-exact linear differential equation  [ytan(x)(cos(2x))-1]dx+csc(2x)dy=0 when…

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Q: Find the implicit solution of the differential equation (1+sin(y))dx + (1+x cos(y))dy = 0.

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Q: Solve the differential equation A. y = x² +cos3x + C B. y = x² + cos 3x + C dy dx = 2x + sin 3x. C.…

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Q: he differential equation using Bernoulli equation x dy/dx + 6y = 3xy4/3

A:

Q: (군2-1) 을 + 2y3 (+ 1)°

A: Given ODE : (x2-1)dydx+2y=(x+1)2 ⇒dydx+2yx2-1=(x+1)2x2-1⇒dydx+2yx2-1=x+1x-1 Which Linear…

Q: Determine the solution of the 1st Ordered Differential Equation: (x - y)(4x + y)dx + x(5x - y)dy = 0

A:

Q: State the order of the differential equation (t +t)y" + (sin t)y' = 2e¹.

A: For a Differential Equation , Order is the highest power of the derivative Degree is the power on…

Q: Find the homogeneous differential equation whose general solution is y = 3cos(x) - e3x/2 -…

A: Given the solution of a homogeneous differential equation   y = 3cos(x) - e3x/2 - 4xsin(2x) Find the…

Q: y' + (2 tan x)y = cos³ x = COS" X

A: The correct answer is option (I) , i.e.  y = (cos²x)(c+sinx) The detailed solution is as follows…

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.