In Exercises 33–36, solve the given differential equations (a) by varia- tion of parameters and (b) by the method of undetermined coefficients. dy 33. dx? dy = e* + e* dx 34. dx? d²y 4 + 4y = 2e2r dy d?y dy d²y dy 35. 4- dx 5y = e* + 4 36. *dx 9- 9ex dx2 dx

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A: General solution to a nonhomogeneous linear differential equation a2(x)y''+a1(x)y'+a0(x)y=r(x) is…

Q: Solve the differential equation with initial condition dy 7y²x3 dx %3D У (2) %3D 3

A: The main objective of the question is to establish relation between x and y.

Q: Evaluate the differential equations: Integrating Factor by Formula a) (2y2 + 2y + 4x2)dx + (2xy +…

A: Given:  a) 2y2+2y+4x2dx+2xy+xdy=0b) y2cosxdx+4+5ysinxdy=0

Q: Solve the differential equation du/dt = (2+t^4)/(ut^2 + u^4t^2)

A: Solve  dudt=2+t4ut2+u4t2 isolate du with 'u' terms on the left side and dt with 't' terms on the…

Q: du 1 + tª dt ut² + u*t² 4,2

A: Let us consider the differential equation dydx=f(x)g(y) To solve the equation using the variable…

Q: Find the solution of the differential equation that satisfies the given initial condition. dy %3D…

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Q: Solve the second order differential equation y + 2y = 3 cos 2x A:y = c, cos(vZx) + cz sin(vZx) +…

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Q: Exercise 2.7 dy 2cosx-sin². -sin x+ y 1. Verify that y, = sinx is a solution to and solve the %3D…

A: Note:- As per our guidelines, We can answer the first question since the exact one wasn’t specified.…

Q: The differential equation y²x + 2y'eª = 0 is Select one: Linear Exact Seperable Homogeneous

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Q: Exercise (2): Determine whether the differential equation is linear or nonlinear: (1) (1- )y" - 4ry…

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Q: test whether the differential equations are exact and solve those that are. 2Y dy 0 dt+-

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Q: The solution of the differential equation dy dx 6. is 6x + C 6lnx + C | 4 6x + C 5 6lnx + C 2

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Q: In Exercises 2, write an equivalent first-order differential equation and initial condition for y.…

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Q: > Solve the non-exact differential equations (Apply Rule III) 1. (x² + y² + 2x)dx + 2ydy = 0 [Ans.…

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Q: Solve the ff. differential equations by applying the appropriate substitution. dy = 2+y-2x+3 1) dx…

A: Since, you have asked multiple questions as per company guidelines, we will solve the first question…

Q: Find a suitable form for particular solution of the differential equation y" - 4y' + 13y te"…

A: 1st is correct answer see the solution on step 2

Q: Solve the initial velue seperable first order differential equation. -Solve for y by using the…

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Q: Solve the differential equation by using variation of parameters: d'y dy 3 dx 3x + 2y = e dx .A 3x y…

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

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Q: Apply the Euler-Cauchy method to obtain a numerical solution of the differential equation for two…

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Q: Solve the differential equation (2x + y) dx - O a. 5x+10y + In |10x O b. O c. 5x O d. 5x (4x + 2y -…

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Q: Find the general solution of the differential equation: dx/dt = 5x - 3. (1/5)[In(5x + 3)]= t + c O…

A: Given that: dxdt=5x-3

Q: Determine the solution of the differential equation 2y"-3y' + 4y = 0 3x V23 y = e (C, cos x+ C2sinx)…

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Q: Obtain the solution to the differential equation: (3x²y² + 2y³)dx + (2x³y + 6xy²)dy = 0 x³y² + 2xy³…

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Q: Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate…

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Q: The solution of the differential equation + 25y 0 is dy Oy= Acos25x + Bsin25 O y (Ar + B)e 5 O y=…

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Q: Solve the Euler-Cauchy differential equation d²y dy 3x- +4y = In2x- Inx %3D dx

A: Given: Let us assume, x2d2ydx2-3xdydx+4y=ln2(x)-ln(x)......(1)

Q: in the form of differential equation shown below; where the initial conditions are z d²y dy + 10 dt…

A: In the given question, concept of Laplace Transform is applied. Laplace Transform The Laplace…

Q: Exercise: 11 [ Solve the non-exact differential equations (Apply Rule IV)] 2. (xy³+y) dx + 2 (x²y²…

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Q: The solution of the differential equation + 2y = a is, Oy = +c Oy= Oy = Oy= T

A: The objective is to find the solution of the differential equation.

Q: Find the general solution of the differential equation: + 16y = 0 Oy= et (C1 sin x + C2 cos a) Oy=e…

A: Given differential equation is 2nd order linear homogeneous differential equation equation with…

Q: u" (x) = e", 0 < x < 1, u' (0) = u(1) = 0.

A: Given: u''x=ex, for 0&lt;x&lt;1 Integrate on both sides as, ∫u''xdx=∫exdxu'x=ex+C1…

Q: 2. Find the particular solution of the differential equations that satisfies the initial conditions.…

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Q: What is the auxiliary equation associated with the second order linear differential equation d^2x…

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Q: 9t y - 9 y = e3t

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Q: 2:- A. Solve the following differential equations using variation of parameter Method: Mads) d²y 1.…

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Q: EXERCISES 1. Use the method of separation of variables to find the general solution to the following…

A: Here we use the method of seperation of variable to find the general solution of the differential…

Q: Use Galerkin's method to formulate a linear finite element for solving the differential equation d'y…

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Q: A student is solving a Cauchy-Euler differential equation and obtains the following solutions of the…

A: Use the cauchy Euler method to solve this problem.

Q: Solve the system of ordinary differential equations defined by dx/dt+y = cost dy/dt+x = −sint

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Q: Obtain the general solution of the following differential equations. 4. x(x² + y*)*(ydx -xdy)+y°dy =…

A: We have given differential equation ,  xx2 + y22ydx - xdy + y6dy = 0 Clearly , this is homogenous…

Q: Find the solution of the differential equation that satisfies the given initial condition. dy = (8x…

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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: . Find the explicit general solution to the given differential equation. Hint: Linear DE. (2x + 1)y'…

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Q: A. Obtain the differential equation of the gi- (1) 3x² – xy² = c (2) y = a cos(x +B) (3) y = c,e¬2x…

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Q: What is the particular solution to the dy dx a°+3 with the 3y differential equation initial…

A: The differential equation dydx=x2+33y is separable because it's the form of dydx=f(x)g(y) where…

Q: Determine the solutions of the 1st-order linear differential equations below: (a) (x +3y)− x y′ = 0

A: Explanation of the answer is as follows

Q: Exercise (4): Show that: (1) y= x c e-*dt is a solution of the differential equation xy – y – x²e-²…

A: As per company guidelines we can solve first question. I hope that the given solution will help you.…

Q: Exercise 1 Consider the differential equation: y®) – 16y" = 3-2e+Gr sin 2r By using the method of…

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