can you show me the step by step solutions: Solve the homogeneous second-order linear ODE:y′′ − 5y′ + 6y = 0 2. Solve the initial value problemy′′ + 4y′ + 4y = 0, y(0) = 1, y′(0) = −2

Q: Find the general solution to the equation xdx + -dy= 3dy O x=/2y+ Cy-2 O xy= 2y + C O y = 2x3 + C…

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Q: 1. (2x-y) dx +(4x+y-6)dy=0

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Find the general solution  y ′ + 4ty = ty2 + t

A: Given differential equation is  y'+4ty=ty2+t to find the general solution of this equation

Q: The general solution of the second-order ODE d²y dx² dy dx can be written in the form 10- + 29 y = 0…

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Q: Differentiate with respect to x: 3x4 x³y + 4y³ = 6 Select one: the following implicit equation for…

A: implicit derivative of y(x) for 3x4-x3y+4y3=6

Q: Solve the given equation.. (3x2 + y)dx + (x²y – x)dy =0 Y +3x = C a. b. x²y? + x²y+ x4 = C C. d.…

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Q: 3 Find the general solution of the third-order ODE y(³) + 6y" + 10y' + 6y = 0, note that m³ + 6m²…

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Q: 6. The three solutions of the equation f(0) = 0 are 0°, 180°, and 360°. Therefore, the three…

A: Given,         The three solutions of the equation fθ=0 are 0°,180° and 360°.          Then fθ-30°=0

Q: Find the general solution of the following DES. 7. (8x¹y6 + 3x³) dx + (12x5y³ + 3xy²) dy = 0 8.…

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

Q: Which of the following equations has a solution of the form F(x,y) = C dy A. 2x + 3y + (2y + 3x); =…

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Q: Determine the general solutions of the following 5. (D3 – D2+ D– 1) y = 4 sin x non homogenous…

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Q: What was the 1-hour growth factor for the bacteria's mass?

A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…

Q: canonical form

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Q: Which of the following equations has a solution of the form F(x,y) = C A. 2x + 3y + (2y + 3x) dy B.…

A: we need to find out at which of the equations has solution of the form F(x,y)=c

Q: A. Solve the following equations: 1. (Dª + 3D³ – 6D² – 28D – 24)y = 0

A: "Hey, Since there are multiple questions posted, we will answer first question. If you want any…

Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

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Q: 5. Find f'(x) if f(x) = √4sin²x +9 cos²x. Solution: U= du dx B) Implicit Differentiation Example:…

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Q: 6. Write a 2nd order homogeneous (not the substitution meaning for homogeneous here - how we used it…

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Q: . Find the general solution of the third-order ODE y(4) — 5y(³) + 6y″ + 4y′ − 8y = 0, note that m² −…

A: Given the third order ordinary differential equation, y4-5y3+6y''+4y'-8y=0. To find the general…

Q: Solve (1- + xp z_(hx [y² + x² (1 1)-2] dy : dy = 0 xy)

A: We have to solve the given differential equation.

Q: y²dx+x(x+y) dy=0 A xy² = c(x+2y) x²y=c(x+2y) xy² = c(2xy) x+y²=c(2xy) B C D

A: Given: The equation is y2dx+x(x+y)dy=0. To find: The correct option for the solution of the given…

Q: (a) Find the general solution of the following equation: y(3) + 5y" + 3y' – 9y = -27x +9+32e". %3D

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Q: Solve completely the following problem. 1. (D² + 2D- 15)y 0

A: Topic = Differentail equation As per guidelines , At a time only one question can be answered.…

Q: Solve the following DE: (1+ y² + xy²) dx + (x²y + y + 2xy) dy=0 O2y²+x²(1+x)²=C O 2y²+x²(y + x)² =c…

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Q: Solve the following homogeneous ODE y- бу + 9у %- 0 with the following initial conditions y(0) = 0…

A: To solve the given differential equation