Find the equation of the line tangent to y = x2 – 3x – 5 and parallel to the line y = 3x – 2. (SOLVE BY USING DIFFERENTIAL EQUATIONS)

Q: Solve by applying "Differential Equation using Substitution Suggested by the Equation"…

A:

Q: Find a differential equation whose general solution is y = C₁e6t + c₂e-4t y" - 2 y' - 24 = 0 X

A: The solution of the DE is: y=c1e6t+c2e-4t where the solutions to the auxiliary equation are 6 &…

Q: Find afunction yp that is a solutionto the differential equation,y′′+y′=2e2x+cos(x).

A: To find the solution y"+y'=2e2x+cosx

Q: dy y3 dx x3 + xy² II

A: Given: - The differential equation is, dydx=y3x3+xy2 To show: - The given differential equation is…

Q: 3. y?dx + (x² + 3xy + 4y²)dy = 0; when x = 2,y = 1

A:

Q: Determine whether the function y = 3 sin 2x is a solution of the differential equation y(4) − 16y =…

A: Consider the given differential equation:

Q: Determine whether the function y = x3 is a solution of the differential equation 2xy′ + 4y = 10x3 .

A:

Q: solve xdx+ydy=a^2(xdy-ydx)/(x^2+y^2) using exact Differential Equation

A: Given equation is x dx+y dy=a2x dx-y dyx2+y2.

Q: Solve by applying "Differential Equation using Substitution Suggested by the Equation" (2x + y)dx–…

A:

Q: Solve the differential equation by variation of parameters. y" + 2y + y = et In(t) y(t) = Submit…

A:

Q: Determine the form of a particular solution (without computing the coefficients) to the differential…

A: The given differential equation is y''-14y'+49y=3te7t

Q: Solve the differential equation by variation of parameters. 1 y' + 3y' + 2y 6+e*

A:

Q: Find a differential equation whose general solution is y = c₁e³t+c₂e-2t 2 = 0

A: We need to determine a differential equation corresponding to the general solution: y=c1e5t+c2e-2t.

Q: Find the general solution of the differential equation. Use C, C1, C2,⋅ ⋅ ⋅to denote arbitrary…

A: y''(t)=60t4-4+12t-3 We need to find the general solution of the given differential equation using C,…

Q: Solve the differential equation by variation of parameters. 1 y" + 3y' + 2y 9 + e*

A:

Q: Find the differential equation whose solutions correspond to the following equation. y = C1x^2 +…

A: For the solution follow the next step.

Q: Solve the Differential Equation using VARIATION OF PARAMETERS: 2y''+18y=6tan(3t)

A:

Q: equation

A:

Q: 2y Find all solutions of the differential equation y' + = 2x/y.

A:

Q: Solve the differential equation by variation of parameters. 4y" – y = ex/2 + 4 y(x) =

A: We have to solve the differential equation

Q: a. y = C,e=x + Cze-2x + x

A:

Q: 2xdy + y Cyz Inx -1) dx = 0

A:

Q: Find a differential equation whose general solution is y = c₁est + c₂e-2¹. 5t = 0

A: I have given the answer in the next step. Hope you understand that

Q: Solve the differential equation by variation of parameters. y" + 2y' + y = e-t In(t) y(t) =

A:

Q: Find the differential equation whose general solution is y=c1e4t+c2e-5t

A: Find the differential equation of given solution.

Q: Find the differential equation having the solution as: a. y = C,e¬x + C2e¬2x + x b. y = C, + C2e³x

A:

Q: Solve the differential equation by variation of parameters. y" + 3y + 2y = 8 1

A:

Q: Find a differential equation whose general solution is 9t y = c₁e⁹t + c₂e-²t = 0

A:

Q: Use variation of parameters to solve the differential equation x²y" + 10xy' + 8y = x².

A:

Q: Solve the differential equation by variation of parameters. y" + 2y + y = e-t In(t). -t 2e t²ln t…

A:

Q: y = cje* + cze²r y" -y – 2y = 0 O 2y " -y' – y = 0

A:

Q: -3z y" + 6y' + 9y = for a> 0.

A:

Q: Find the differential equation having each equation as general solution. 7.) y= x + C,x + C,e 11.)…

A: An ordinary differential equation is an equation containing independent variables, dependent…

Q: Find the linear, nonhomogeneous differential equation with constant coefficients whose solution is y…

A: Given: yt=c1et+c2e2t-3tet+cost-e-t2          ...... (1) Solution: Differentiate equation (1) with…

Q: For which value of the constant c is the function y = 15e-® + x + c a solution of the differential…

A:

Q: Determine the function y = y(t) that solves the differential equation y' – 3y = t and has y(0) = 3.…

A:

Q: s, p°+ 3 xp²- yp²-3xyp = 0 find the differential equation

A: Given: p3+3p2−y3p2−3y3p=0 The standard notation for p is p=dydx.

Q: Find the differential equation having the solution a. y = C,e¬* + Cze=2x + x b. y = C, + C2e³x

A: Explained below

Q: 2)By using y' = p substitution, solve the differential equation xy" = y' + x(y')².

A:

Q: Use variation of parameters to solve the differential equation: -2x y" + 4y' + 4y : In x. = e

A: Here I am attaching image so that you understand each and every step.

Q: Find the general solution of the differential equation. Use C, C1, C2,⋅ ⋅ ⋅to denote arbitrary…

A: the given differential equation is: y'(t)=12t5-20t4+2-6t-2 we have to find the general solution of…

Q: At what point of the curve y = x3 + 3x are the values of y’ and y” equal? (SOLVE BY USING…

A: This is a basic derivative problem where we need to satisfy the given condition

Q: Solve the differential equation using Method of Undetermined Coefficients and by Inspection. (D³ +…

A:

Q: Determine whether the function y = 2 sin 2x is a solution of the differential equation y′″ − 8y = 0.

A:

Q: Solve the differential equation using inspection method d'y d³y = 24. dx5 dx³

A:

Q: Solve the differential equation by variation of parameters. y" + 3y' + 2y = 3 + e* y(x) =

A:

Q: (2x+ykdx– 3(2x+ y+4)dy=0 1.

A: Note: We are required to answer only the first question, unless specified.

Q: Find the general solution of the differential equation: y' – 5y = xy. - Use lower case c for the…

A: The given differential equation is y'-5y=xy2 This can  be written as dydx-5y=xy2 Divide both the…

Q: Solve the differential equation by variation of parameters. y" + 2y' + y = e-t In(t) y(t) = %D

A:

Q: Find a differential equation whose general solution is 6t y = c₁et + c₂e -3t = 0

A: We find a differential equation whose general solution is y=c1e6t+c2e-3t.