Find the solution on the differential equation using suggested substitution.

Q: 5x y = C, + C2e4x 4

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Q: Find the differential equation whose solution is given by: y^2=4ax

A: To find the differential equation for y2=4ax differentiating this equation with respect to x.

Q: Find the solution of the given differential equation

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Q: Find the general solution of the differential equation. 1 こ

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Q: Determine an appropriate substitution and then solve the differential equation. ху'%3D у In(ху)

A: We will substitute v = xy to solve the given differential equation. after substitution the…

Q: dy 2. dr 2xy

A: Given : dy/dx - 2xy = ex²

Q: Solve the differential equation with clear steps

A: Given, system of differential equation is dxdt=3x-y-zdydt=x+y-zdzdt=x-y+z We can write it as in…

Q: • / = Ity

A: y'=x-yx+y It is a homogeneous differential equation. Put, y=vx⇒y'=v+x·dvdx Therefore,…

Q: Find the differential equation that has y = C1 + C2x as its general solution.

A: To find the original differential equation we  have to eleminate the arbitrary constants by…

Q: Find the complete solution of the differential equation, y' = 2 - cot.

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Q: y = Ae* + Be-*

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Q: Find the differential equation whose general solution is y = C1x + C2ex. %3D

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Q: Solve the given differential equation by undetermined coefficients.

A: Given,              y''-2y'+2y=e2xcos(x)-4sin(x).

Q: Find a differential equation whose general solution is y = cie®t + cze¬,

A: The complimentary function of the differential equation if the root of the auxiliary equation are…

Q: Determine the general solution of the given differential equation

A: Rewrite the equation in standard form. And solve it

Q: Find the solution of the differential equation that satisfies the given initial condition. dP

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Q: Show that the differential equation UTM dy -2 - ye rey - 2y dr is exact and find its solution.

A: Use the concept of exact differential equations.

Q: differential equation by using an appropriate substitution.

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Q: Find the particular solution to the differential equation when y(0)=3 and (2)=1

A: Given differential equation isy''=y'2x-y'x2-1 The conditions are y(0)=3,  y'(2)=1

Q: Solve the differential equation by using the linear equation method 2r dt +4

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Q: Find the order of the differential equation. And check if it is linear or nonlinear.

A: Given the differential equation

Q: Formulate a differential equation that is satisfied by 1. y=Ae2+ Bxe²r

A: To find: The differential equation: Given: The equation is y=Ae2x+Bxe2x. Concept used: Product rule:…

Q: Find a differential equation whose general solution is y = cie" + cze *. = 0

A: To find a differential equation whose general solution is given by, y=c1e7t+c2e−3t

Q: у" — Зу" + Зу' — у %3D х — 4е* -

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the solution to the differential equation   that passes through the origin.   z=

A: As the solution function to the given differential equation, passes through the origin we will have:…

Q: Solve the differential equation using only methods taught in class. y' + 3xe' = 0

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Q: Find the general solution for the differential equation

A: Given: The given differential equation is X'=45-26X

Q: Find the general solution of the differential equation

A: We have given differential equation drds=49r We have to find general solution of differenial…

Q: Find the general solution of the differential equation with clear steps.

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Q: Find a differential equation whose general solution is y = ciet + cze-4t. %3D

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Q: (0.g)=

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Q: y = Clx+ C2e

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Q: Find the particular solution to the differential equation y'=2x passing through the point (2,7)

A: given differential equation is y'=2x we can write it as dydx=2xdy=2xdxy=x2+c

Q: Find the solution of the given differential equation.

A: Here in order to solve this differential equation, we will first check that the differential…

Q: Vyy" – 1 = y'

A: Given DE is  √(yy''-1) = y'' ......(1)

Q: Find the solution of the differential equation that satisfies the given initial condition.

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Q: Find the general/particular solution of the given differential equation:

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

Q: у" - Зу' + 2у %3Dcos(e -*)

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Q: Solve the given differential equation by separation of variables. ds dr = KS

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Q: 21

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Q: 4te dt TOT

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Q: The roots of an auxiliary equation are m1=4, m2=m3=-5. What is the corresponding differential…

A: If the root of the auxiliary equation is m1=α and m2=β, then the corresponding differential equation…

Q: Find a differential equation whose general solution is -4t y = cjet + cze¬4.

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Q: Find the differential equation whose solution is given by y^2=4ax

A: topic - differential equations

Q: Hi, can I get help with this problem? Thank you! 3.4

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Q: If we use the method of undetermined coefficients, the particular solution of the following…

A: y(5)+y(3)=x+cos(x) Particular solution : As equivalent function containing x so (To maximum order to…