Verify that the indicated function is an explicit solution of the given differential equation. y''''=y+tanx(2sec^2(x)-1);      y=-cos(x)*ln((1+sinx)/(cosx))

Q: Find the particular solution that satisfies the initial condition: Differential equation: 2xy' - ln…

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Q: Find the Differential equation by eliminating the arbitrary constant  x2-y2=a2

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Q: 3. y'-5y = x*e* - xe* – xe³x

A: 3. the given differential equation is y'-5y=x2ex-xe5x

Q: Find the differential equation whose solution is given by y = C,et*cos3x + C,e*sin3x

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Q: In y = C₁e* + C₂е¯x

A: Given problem:- Find its differential equation through eliminating arbitrary constants.    In(y) =…

Q: By using suitable method, form an ordinary differential equation by eliminating constant A from the…

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Q: y using an integrating factor, find the general solution of the differential equation dy/dx…

A: Given differential equation :                          dydx-ytanx=sinx

Q: y = -CI cos 3x + C2sin 3X

A: Given, y=c1cos3x+c2sin3x We have to find the corresponding differential equation by elimination of…

Q: Form the differential equation whose primitive is given by y= ex(a cos⁡x + b sin⁡x),  a, b, being…

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Q: Given the differential equation: D(sin x-cosx+3e +x) What is the second derivative?

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Q: Find the particular solution that satisfies the differential equation and the initial condition.…

A: f(x)=∫f'(x) dxf(x)=∫(16x3-6x)dxf(x)=16x44-6x22+C              (∫xndx=xn+1n+1)f(x)=4x4-3x2+C where…

Q: A: By using Linear equation solve the first order differential equation y' + sec(x)y = cos(x)

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Q: he population y(t) of a certain microorganism grows continuously and follows an expo uadrupling time…

A: In this question, the concept of derivatives is applied. Derivative We can use a derivative to…

Q: y = 2xy -x

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Q: Solve the differential equation defined by x dy/dx −2y = x^6 sinx.

A: Consider the provided differential equation,

Q: Explain how to solve a separable differential equation of the form g(y) y'(t) = h(t).

A: A separable differential equation is one in which the terms of two variables in the term can be…

Q: Find the ordinary differential equation from the general solution: y = Ae-* + Be-*

A: Since you have posted multiple questions and we can answer one question. So, answered first…

Q: 1. Form the differential equation by eliminating the constant A and B from y = emx (A cos nx + B sin…

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Q: Solve for differential equation of (y/x + 6x) + (ln x - 2)y′ = 0

A: Explanation of the answer is as follows

Q: Find the differential equation by eliminating the arbitrary constant/s. y = = Aex cos x + Bex sin.x…

A: We differentiate the number times as the number of arbitrary constants present in the equation and…

Q: find solution of this differential equation:  y′ tanx sin2y = sin^2 x + cos^2 y

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Q: y = C, x? sin 4x + C2x² Cos 4x

A: The equation is y = C1x2sin4x+C2x2cos4x

Q: (D² + 4)y = Sinx

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Q: By climinating the arbitrary constants, form the differential equation in the fotowng cases: 1- y2 A…

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Q: 2. Solve the differential equation dy -e2y-cotx tan x dx

A: On differentiating the given equation, tan2 x.dydx=e2y.e-cotxe-2ydy=e-cotxtan2x.dxLet, cotx=t…

Q: Solve the higher differential equation below; yiv - y = 2 cos x

A: The given differential equation is yiv-y=2 cosx The auxiliary equation is  m4-1=0. On solving,…

Q: 1. x In x sec² y dy + [tan y – (In x)°]dx = 0 When:x = 1; y = "

A: The given differential equation is solved below in detail.

Q: the given differential equation is not exact and hence show that Solve it x²ydx -lx3+y?)dy=0

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Q: Solve the differential equation (yexY+cosx)dx + xeXYdy=0 O Inxy+cosx O exy+cosx = 0 O exy+sinx = 0 O…

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Q: Find the solution to the differential equation dy/dx=19xy/(lny)4 which passes through the point…

A: Separate the variables than solve the differential equation by integrating both sides.

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: Solve the first order linear differential equation. dy - (cotx)y = sin³ | dr

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Q: 3. Show that the differential equation zxy

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Q: Find the differential equation by eliminating the arbitrary constant/s. 1. ecosx = c(1-cosy)-¹

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Solve the differential equation by variation of parameters. y" + y = csc(x) y(x) = c₁cos(x) +…

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Q: Give the general solution of the differential equation y'-y = sinx + cos2x +e-x

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Q: Form the differential equation by eliminating arbitrary constants:y=ax3+bx2

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Q: Find the particular solution that satisfies the differential equation and the initial condition.…

A: To find The particular solution that satisfies the differential equation and the initial condition.

Q: Find the Differential Equation of (sin2x-2ycosx)dx=2dy

A: First we compare given differential equation with dy/dx+Py=Q and find integration factor using…

Q: By first finding an integrating factor, solve this differential equation. Give your answer in the…

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Q: Find the solution on the differential equation using suggested substitution.

A: The given differential equation is:yxtanx+lnydx+tanxdy=0We need to solve the above equation.

Q: Find the differential equation whose complete solution is y=c1e-x+c2ex+4x using elimination of…

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Q: Find the differential equation using elimination of arbitrary constants

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Q: Solve the differential equation tan x- dy ey-cotx dx

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Q: a. Obtain the differential equation of the family of straight line with the algebraic sum of the…

A: Write general equation first of given conditions.

Q: Find the Differential equation by eliminating the arbitrary constant x2 - y2 = a2

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Q: 3. (sin'x + cosv)dx - tanxsin2ydy = 0

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Q: y"-4y = 0; cosh 2.x, sinh 2x

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Q: Obtain the Differential Equation from the given general solution. y = C¡ cos(4x) + Cz sin(4x) + Cx…

A: Use the following formula, to find the solution. ddxcosax=-asinaxddxsinax=acosaxddxuv=udvdx+vdudx

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.