Show by direct substitution that is a solution of y" +xy=0 and write the general solution.

Q: Determine by substitution if y(x) =xe* is a solution of y"- 2y' +y = 0 %3D

A: Given  The differential equation is y''-2y'+y=0

Q: Find the particular solution of xy" + xy' 13; y = 0 and y' = 1/2, when x = 1.

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Q: Use separation of variables to find an explicit solution. xyy' = 2xy + y?

A: Idea: after separating x,dx and y, dy terms together. we take integration on both sides . after…

Q: Solve the given DE: 2ydx=3xdy, when x-2, y=1. O y=(x/2)^(2/3) O y=(x/2)^(1/3) O y=(x/3)^(2/3) O…

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Q: Show that y = ex + 3xex  is a solution of y"-2y'+y=0

A: The given differential equation is,

Q: Let y(x) be the solution for the DE : y' = (x + y – 1)² If y(0) = 1, then find y()

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Q: (c) xy' = y(3– x)

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Q: у" + 2y' +y = 4e' ¬x

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Q: By direct substitution, show that y = Jo(x) is a solution of the DE: x²y" + xy' + x²y = 0

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Q: Show that y = 5x2 + 2 is a solution to the DE xy' +(2)/(5) y" = 2y.

A: To show: y=5 x2+2 is a solution of differential equation xy'+25y''=2y

Q: Let y(x) be the solution for the DE : y = (x + y – 1)2 If y(0) = 1, thenfind y(4)

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Q: Find the general solution to: y(x² +1) + y' = 0, for y > 0.

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Q: with solution Final dy वर di dr-/2cset-1 de lesct. +2

A: We have to find out derivative

Q: What is the solution (ry – r) dr + (x²y + y) dy = 0 when 2 and y = 1

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Q: Show by direct substitution that is a solution of y" +xy=0_ _and write the general solution.

A: Given that, y=xj1323x12 And the given differential equation is, y''+xy=0...1 The solving by power…

Q: Solve xyy'=1+y^2, for y=3 when x=1, or y(1)=3

A: The given differential equation with initial condition is: xyy'=1+y2 where y1=3.…

Q: Verify that y = c is (1+ce') (1– ce') is a solution to y' = + (v² – 1) , where some constant.

A: For verifying given thing, we find solution of given differential equation Now, for finding solution…

Q: Given that d²y 2. +y =0. dx2 Show that y = x is not Solution a

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Q: Find a second solution to 4x²y" +y = 0, given one solution y1(x) = x!/² In x.

A: Given differential equation 4x2y''+y=0.....1 And given one solution is y1x=x12lnx Equation (1) can…

Q: 2. JO (y+5) dy (y-3)

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Q: Let y(x) be the solution for the DE: y = (x+y+ 2)2 If y(0) = -2, then find y() %3D

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Q: Find the solution of y' + p(x) = 4x if y(0) = 3 and where

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Q: solve by bernoulli y' + (8/x)y = x6y4

A: We will find out the required general solution for given Bernoulli's equation.

Q: Determine the type of DE/method of solution to be used and solve. y′ = x3 − 2xy, when x = 1 and y =…

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Q: Check that y Cx) = e* is the Solution of y" + y' - 2y = 0

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Q: y" — 5y' = x − 2, when x = 0, y = 0, y' = 2

A: To find the particular solution for the given DE.y''-5y'=x-2, when x=0, y=0, y'=2

Q: 8x²y" + 10xy' – (1+x)y = 0

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Q: Suppose that the DE y"" (x) + 7y(x) =70 2³ +123 has a solution of the form y = Az³ + B Find the…

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Q: у" — у' — х %3D 0

A: We are given: y'''-y'-x=0⇒y'''-y'=x Auxiliary equation is : m3-m=0⇒m(m2-1)=0⇒m=0, 1, -1 Hence,  CF=…

Q: (D² – 3D + 2)y = e2×(1 + e2x)¯ -

A: Given: D2-3D+2y=e2x(1+e2x)-1 Formula used:y=yh+yp

Q: The solution of the DE (1+ cot²x)y' = cscx coty is

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Q: Obtain the general and particular solution 1. 2ydx = 3xdy, when x= 2, y = 1.

A: The given differential equation,1. 2ydx=3xdy, when x=2, y=1 Note:     Multiple questions are given,…

Q: what is the privet Solution to the equation (0'+0)y(x)=Xsinc) (X)

A: The given differential equation is D3+Dy(x)=xsin x The particular integral of vsin x , where v is…

Q: Obtain the particular solution of x²y" + xy' = 1; y = 0 and y' = 1/2, when x = 1

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Q: -Find the solution of y"+y' + by = 0 by transforming y = x"u|

A: Put y=xαu in the given equation y'=xαu' y"=xαu" Then the equation becomes xαu''+axxαu'+bxαu=0 Now…

Q: y" + 2y" + y" = x + eX %3D

A: Given the differential equation y'''' + 2y''' + y'' = x + ex We find the particular solution form…

Q: Find the general solution of the DE: y" + y" – 16y' + 20 = 0.

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Q: If f(s) =S+ 25-7, what is Lurite solution in exact form.

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Q: Verify that for x>0, (2/ /3)x³² 2 is a solution of the equation yy" =x.

A: Given:     To verify: y is the solution of equation yy''=x

Q: (x² – 1)y" + 2y' – (x – 1)(x + 1)² = 0

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Q: Use the SUBSTITUTION METHOD to solve for y: x + 2y = 3 %3D X = 4y

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Q: Use separation of variables to find an explicit solution. xyy' = 2xy 2 2 + y?

A: using seperation of variables  and then integrate....

Q: Verify that y = c₁ex + c₂e4x is a solution to the DE: y" - 5y + 4y = 0.

A: We are authorized to answer one question at a time, so we are answering the first one, please repost…

Q: Consider the IVP: y" + 9y = 40ex ; y(0) = 5, y'(0) = -2. Find the general solution.

A: Use the given differential and initial conditions.

Q: Find the general solution of (x³ + 2y4)y' = 3yx² in implicit form f(x, y) = c. When y(0) = 1, what…

A: We have to solve the differential equation

Q: let y"(x) + y(x) = 0 be given What would be a suitable solution y(x)?

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Q: Determine if y=ex −7x−4 is a solution to y′−y=7x−3.

A: To test whether the given function y(x) is a solution of the given differential equation

Q: Show that y = c1ex + c2e-x + c e + 3 is a solution of y ||| -2y | | - and | + 2y = 6 (justify).

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Q: Show by direct substitution that y =/x J/3(x/2 ) is a solution of y" +xy=0 and write the general…

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

Q: Is it true that the solution set for x ≥ 0 is placed above the y – axis?

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