Check that the indicated function is an explicit or implicit solution of the given differential equation. d'y + 2x d’y dy X- xp dx +y=12x ; y=c,x+c,x +c,x In x + 4x² a)

Q: Find the solution of the differential equation xyy' = x² + 1 that satisfies y(e) = e O A. y = Vx2…

A: Option " B " is correct answer. Thankyou !

Q: Find the solution of the differential equation that satisfies the given initial condition. dL KL2…

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Q: c. x²y″ − 3xy' +4y=0, _y(1)=5, y′(1)=3. - - d. x²y" — 5xy' + 8y =8x6, y(½)=0, y′(½¹⁄) = 0.

A: (c) A differential equation is given by, x2y''-3xy'+4y = 0 with initial conditions y1 = 5 and y'1 =…

Q: 5. Verify that the indicated pair of functions is a solution of the given differential equation on…

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Q: Verify that for constants A, B, C and D the function ø(x) = Ae* + Be* + C sinx+ D cos x is a…

A: ANSWER :

Q: Determine whether the function y = x2 ex + sin x + cos x is a solution of the differential equation…

A: Here given function as y = x2 ex + sin x + cos x .....(1)

Q: a. Verify that the indicated family of functions is a solution of the given differential equation.…

A: To verify that the indicated family of functions is a solution of the given differential equation.

Q: Find the general solution of the given higher-order differential equation. du, dzu d?u - 2u = 0 dr?…

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Q: 12. y" + (y')2 +1 0; y In cos(x-c) + C2

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Q: Show that the function: y = -xcos (x) – x is a solution to the differential equation: dy :) = y + x²…

A: Let's find.

Q: Find the solution of the differential equation that satisfies the given initial condition. x In(x) =…

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

A: The given differential equation is dLdt=kL2lnt  Initial condition L1=-1.

Q: Suppose the roots of the auxiliary equation are at iß. These are unequal roots, the general solution…

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Q: Find the solution of the differential equation that satisties the given initial condition. dL kĽ² In…

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Q: 1 (c) y' + 2kxy? = 0, y(x) = %3D 1+ kx?

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Q: Verify that the function is a solution of a DE. Show your solution. Solution Differential Equation y…

A: As per our guidelines, we are supposed to solve only first three parts. Kindly repost other question…

Q: Find the solution of the differential equation (In(y))6 dy dx = x°y which satisfies the initial…

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Q: Verify that the function y (x) = ln (x + c) is a solution of the differential equation e^y y` = 1…

A: The given differential equation is: ey y'=1

Q: Find the solution of the differential equation that satisfies the given initial condition. x In(x) =…

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Q: By using the substitution z = y², convert the differential equation dy x²y- xy2 = 1. dx to a linear…

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Q: Verify that y = c, sin 3x + c2 cos 3x + 4e* is a solution to the differential equation y"-y" + 3y'-…

A: We have to verify that, y = c_1 sin 3x + c_2 cos 3x + 4e^x ;  is a solution to the differential…

Q: Show that xy = ae" +be* +x is a solution of the differential equation. d'y +2- -x+x-2=0. X dx

A: If we differentiate   the given  solution equation two times  and  get  the given differential…

Q: Given: 1+ ce y = 1- ce 1+ ce y = 1- ce is a solution to the differential equation Show that dy 1 (ỷ…

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Q: 3a. Verify that both yı(x) = 0 and y2(x) = (x – 2)ª %3D are solutions to the differential equation…

A: 3a.To verify that both  y1(x)=0 and y2(x)=(x-2)3 are the solutions of the differential…

Q: dy y X + 2 dx 3. || 3.

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Q: The indicial equation for the differential equation хy" + 5у" - бху %3D 0 is O A. "(5r – 1) = 0 А. O…

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Q: Verify that the indicated function is an explicit solution of the given differential equation.…

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Q: Find the general solution of the given differential equations by the concept of Exact DE and…

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Q: a) Verify that the function = x + is a solution of the differential equation xy' + 2y = 4x², (x >…

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Q: Consider the differential equation dy dy +6y=0. dr2 Enter either of the solutions of the auxiliary…

A: Given d2ydx2+5dydx+6y=0

Q: Show that y = Vx],(Ax), 1> 0 is the solution of the differential equation %3D x*y" + (x²x² – v² +±)…

A: The given differential equation is,  x2y''x+λ2x2-v2+14yx=0 This differential equation can be written…

Q: d²y dy x² +1 -3x xe(0,+0) - 6+9y = e* dx² dx

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Q: determine two linearly independent solutions to the given differential equation on (0,∞). Q.…

A: Consider the given differential equation, x2y′′−x(1−x)y′+(1−x)y =0 Divide both sides of the equation…

Q: satisfies

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Q: Consider the differential equation: dy/dt + ty = e-1/2t^2 ; y(0) = 1 Is y(t) = te-1/2t^2+e-1/2t^2 a…

A: Given differential equation is dydt+ty=e-t22                                 (i) It is a first order…

Q: Find a particular solution to the differential equation using the Method of Undetermined…

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Q: Using the substitution y = vx, show that dv 2x- dr = (v – 1)? Hence show that the solution of the…

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Q: determine the general solution of the given differential equation that is valid in any interval not…

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Q: determine the general solution of the given differential equation that is valid in any interval not…

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Q: Find the particular solution of the differential equation dy (x – 8)e-2y dx | satisfying the initial…

A: W can solve the given differential equation by using the variable separable method.Then apply the…

Q: 3. Consider the differential equation a²y" – x(x + 2)y + (x + 2)y = 0, x > 0 %3D a) Show that yı(x)…

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Q: dy = xe', y(0) = 0 dx %3D

A: dydx=xey⇒dyey=x dx⇒e-y dy=x dx⇒∫e-y dy=∫x dx⇒-e-y=x22+C⇒e-y=-x22-C⇒-y=ln -x22-C⇒y=-ln -x22-C

Q: 5. Verify that the indicated pair of functions is a solution of the given differential equation on…

A: We need to verify that given pair of function is a solution of the given system of differential…

Q: Determine whether the given implicit function is a solution to the given differential equation. at y…

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Q: Verify that the function y = C1e−x cos x + C2e−x sinx  is a solution of the differential equation y″…

A: y=C1e-xcosx+C2e-xsinx Differentiating with respect to x, we get…

Q: Verify that the function c,(x + y)° = xek is a solution of the differential equation (x² + y² }kdx…

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Q: Use the the method of reduction of order to find the second solution of the given differential…

A: Consider second order homogenous differential equation given by, y''+Pxy'+Qxy=0→1 General solution…

Q: Prove or disprove that the function y = t exp is a solution to the differential equation y = y" +…

A: Given differential equation is y=y''+y' ⇒y''+y'−y=0 Write the auxiliary equation m2+m−1=0…

Q: ) Prove that: (y -c} = C x is the solution of the differential equation dy dy 4x 2x dx 0= dx Then…

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Q: | Find the solution of the differential equation (In(y))³ dy = x'y dx which satisfies the initial…

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.