Find the general solutions to the following non-homogeneous Cauchy-Euler equation using variation of parameters. (t^2)z''+tz'+25z=-tan(5*ln(t))

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

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Q: find the differentials of the first and second orders u=xyz

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Q: Find a homogeneous linear differential equation wit Gcosh 2x coc E 2x cin 5

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

A: Given differential equation is homogeneous equation

Q: By separating variables, find the general solution of the differential equation dvc = - dt RC' where…

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Q: Find general solutions of the differential equations in Prob- lems 1 through 30. Primes denote…

A: Given differential equation is Let us take Therefore, given equation become which is linear…

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

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

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Q: Find the general solution of the differential equation with the help of lablace transform

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Q: Find the differential equation of the family of hyperbolas having center at C(0, k), whose…

A: First write the standard equation of hyperbole having transverse axis parallel to y-axis and satisfy…

Q: Obtain the differential equation for the family of circles with center on the line x = 8.

A: The general equation for a circle can be written as

Q: Write down all possible methods in which the (х- differential equation 2x = 2y) dx/dy can be solved.…

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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: Consider the following. Differential Equation Point y' = 4x2 - x (0, 3) (a) Sketch the slope field…

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Q: 3) Find the solution af equation that satisties the qiven mitial condition. of the differential L0…

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Q: What is the differential equation of the orthogonal trajectories of the family of curves y = Cx ?

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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: The differential equation ry" + 3y - 7y=seca is normal on any open interval not containing a = 0.…

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Q: find the differential equation for the following families of curves. 8. Horizontal parabolas whose…

A: Consider horizontal parabolas whose vertices lie on y-axis. The objective of the problem is to find…

Q: Compute the differential dy  for  y=(6x+sinx)^3

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Q: Find the differential of w = ln /x² + 3y² + 2z²

A: Here we use chain rule of differentiation to find the required differential. According to chain rule…

Q: 1. What is the integrating factor of the differential equation ydx – xdy = 0 using case 1?

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Q: obtain in alinear differential eqaution with real, constant coefficients that is satisfied by the…

A: The solution of the problem is given in the next step.

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

A: Given the differential equation:

Q: find the differential equation for the following families of curves. 11. Hyperbolas with vertical…

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Q: Find the differential equation of all circles passing through the origin and having their centers on…

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Q: 6. Why is it very easy to conclude that x2 dx diverges without making any integration calculations?

A: This question is taken from the calculus and sub-topic is improper integral in which we have to give…

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

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Q: Derive a differential equation for the orthogonal trajectories of the family  of curves xy=c

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Q: Show that the integrating factor is secx. Hence, show the full steps to solve the linear…

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Q: Obtain the differential equation of the family of circle with center on the x-axis

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Q: Find the differential of the given functions. 1. y= x-2x² + 5 5. у 3 1- -s2

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Q: Find the differential equation of the family of circles with center on x-axis.

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Q: By using variation of parameters, what is a possible value for u'1 for the differential equation y''…

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Q: (2x sinh2 + 3y cosh?) dx – 3x cosh dy = 0 |

A: Concept Used: For  y'=f(x, y)   ...(*)If f(hx, hy)=hn f(x, y)Then (*) is homogenous equation of…

Q: The integrating factor that transform the differential equation y" +y' + Axy = 0 into a…

A: Given - The differential equation y'' + 1xy' + λxy = 0 To find - The integrating factor that…

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

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Q: Use variation of parameters to find the general solution of the following differential equation: y"…

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Q: Find the differential equation of all sphere of radius 5 having their centers in the xy planes

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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: Use a linear approximation (or differentials) to estimate the given  number. 28. cos 29°

A: In linear approximation, we estimate the value of the given function or number using the tangent…

Q: Find the differential equations having as solution of y = x sin(xtc) .

A: We find the differential equations having as solution of y = x sin(xtc) .

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

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Q: 2. Use the underermined coefficients method to find the goneal Scution of the differential…

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Q: Obtain the differential Equation from the family of ellipses centered at (h.k) whose semi-major axis…

A: Here h,k are parameters ,not constant.

Q: Derive a differential equation for the orthogonal trajectories of the family of curves xy c %3D

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Q: Find the differential equation of all family of circles with center at the line 3y - x = 0 with h…

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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.