Show that every function f is defined by f(x) = (x³ + c)e-3x where c is an arbitrary constant, is a solution of the differential equation dy + 3y = 3x?e-3x dx

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

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Q: Show that the function y = f(x) is a solution of the differential equation.

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Q: y = (C₁ + C₂x) eª + sinx+x²; y" - 2y' + y = −2 cos x + x² − 4x + 2

A: Here we find the first and second derivatives of given solution and then put in the left hand side…

Q: Show that every function f defined by f(x) = (x3 + c)e-3x where c is an arbitrary constant, is a…

A: Differentiate equation, fx=x2+ce-3x with respect to x to get the differential equation.

Q: Prove that the differential equation is not exact ey (e" + ") - s/ = 0 2+ + -

A: Exact diffretaial equation

Q: Find the particular solution that satisfies the differential equation and the initial condition.…

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Q: y = Ce * + C2e 2x + C3e * + e 2x

A: y=c1e-x+c2e-2x+c3e-x+e2xy=c1+c3e-x+c2e-2x+e2x Here, complimentary solution is  y=c1+c3e-x+c2e-2x…

Q: Verify that the function y = 2x - 6x + 10 satisfies the differential equation -y"-xy"-2y' = -24x.…

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Q: Solve the Cauchy-Euler differential equation x -2x+2y = x dx dx

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Q: Verify that the function is a solution of the differential equation.

A: We have to verify that given function y=x lnx-4x is the solution of differential equation: x+y-xy'=0…

Q: Determine whether the given differential equations are homogenous and, if so, solve them. x +y 2.xy

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Q: Find a solution to the differential equation (x + 1)y' + 3y = x such that y(0) = 5. You may assume…

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Q: Verify that each of the given functions is a solution of the given differential equation: x*y" - xy…

A: Here we have to solve the differential equation by substituting the values of both y1 and y2 by…

Q: Verify that the function y = e-3x is a solution to the differential equation d2ydx2 + dydx − 6y = 0.

A: We have to verify the solution

Q: d. 2ydx +x(x² In y – 1)dy = 0 -

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Q: Show that the given function is a solution to the differential equation y=3x2+1, 2ydx-xdy=2dx

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Q: Verify if the given functions are solutions of the differential equation. Also, determine the value…

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Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

A: Given first differential equation(y-x)y'=y-x+2To find: y=x+2x+6 is the solution of the given…

Q: show that each function y = ƒ(x) is a solution of theaccompanying differential equation. y' = y2 y =…

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Q: Determine which function is a solution to the differential equation xy' + 3y = 0. 3x

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Q: Find a second solution of each differential equation. x²y" + xy' + y = 0; y1 = cos (In x). (1+x)y" +…

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

A: Consider the given differential equation: y'x=4tan2x-3cosx Here, the objective is to find the…

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

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Q: Identify the linear differential equations in the following. Justify and show your work.…

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Q: Determine whether the function y = ln x + e2x + Cx4 is a solution of the differential equation y(4)…

A: Given differential equation is y(4)-16y=0 Given function is y=lnx+e2x+cx4 Differentiate y repeatedly…

Q: Verify that the indicated expression is an implicit solution of the given first-order differential…

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Q: 2. (2xy + x)dy – [x² + y² + y + 1]dx = 0 When: x = 1;y = 0

A: The given differential equation is: 2xy+xdy-x2+y2+y+1dx=0 Solve for the particular solution of a…

Q: test whether the differential equations are exact and solve those that are. (x-y) dx + (x+ y) dy = 0

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Q: 10. Determine the differential equation whose set of independent solutions is le, xe, x e)

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Q: Find the particular solution that satisfies the differential equation and the initial condition.…

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

Q: (c) Show that the function is a solution of the differential equation (−1)" x2n f(x) = Σ (2n)! n=0…

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Q: (2xy + x² + x*)dx – (1+ x²)dy = 0

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Q: B.Verify if a given function is a solution to a differential equation. 1 d²y dy 1x². +x=y= ln x dx²…

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Q: show that each function y = ƒ(x) is a solution of theaccompanying differential equation. 2y' + 3y =…

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Q: Find the particular solution that satisfies the differential equation and initial condition. f '(x)…

A: find f(x) where   f'(x)=(x2-2)/x2 ;  x>0  ;f(1)=1 f'(x)=(x2-2)/x2 integrate on both sides…

Q: Solve the Linear Higher Order of differential equation using the formulas below. (D² – D + 3)(x In…

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Q: What is the general solution of the first order differential equation a csc (2) – B da + a dß = 0 if…

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Q: Find the particular solution that satisfies the differential equation and the initial condition.…

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Q: 5. Verify that y = (x³ – x) log cx satisfies the differential equation (x³ – x)y' – (3x? – 1)y = x5…

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Q: Q1. Show that the given function is a solution of the differential equations. y = e-* + sinx y" + y…

A: Given differential equation                                              y''+y=2e-x    or…

Q: Find all solutions to the differential equation. Use c to denote an arbitrary constant. y' = x ln(x)…

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Q: What is the general solution of the first order differential equation a csc (2) – B da + a dß = 0 if…

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Q: y = C1e2" sen(x)+ C2e²" cos(x) +x² + C3x + C4.

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Q: The general solution to the differential equation -9x²y" + 9xy' - 18y = 0 is given by: A) C;(cos…

A: We have to find general solution of given differential equation.

Q: Determine whether the statement "The differential equation y′ = xy − 2y + x − 2 is separable" is…

A: Determine whether the statement "The differential equation y′ = xy − 2y + x − 2 is separable" is…

Q: Demonstrate that the function f(x)= e^-x sin (x) is a solution for the differential equation f(x) +…

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

A: Given that: f'(x)=-4x; f(1)=-1To find the particular solution

Q: 2) x- 1= -0y

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Q: Verify that the indicated relation is an implicit solution of the given first order differential…

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