Determine the longest interval in which the initial value problem is certain to have a unique twice differentiable solution. (Do not attempt to find the solution.) (t-3)y" - 3ty' + 5y sint, y( - 7) = 7, y' ( − 7) = 3

Q: Find the solution. y'+=V5.y(1) = 0

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Q: y' = (1-x)y²+(2x-1)y-x a special solution of the equation y1(x)=1, Find the general solution of the…

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Q: Solve y" + 3y" – 3y' – y = x+ e².

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Q: 4x y" - 5y + 4y = ¹, y(0) = 0, y'(0) = 10/3 e

A: Please find attachment

Q: (1) Find and classify the extremes value of f(x) = 6x* – 4x° over the interval [-2, 2). (2) A…

A: According to Bartleby Q/A guidelines, we only allow solving the first question if multiple questions…

Q: Q7. Solve the Cauchy-Euler equation (i) 4.x²y" + 4.xy' – y = 0. (ii) 4x²y" + y = 0.

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Q: Obtain the particular solution for the equation 2(x³ + 7)y' = x?y when x = 1, y = 4.

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Q: find the seril solution of the equation y``+  4xy = 0  at the point  x0 = 0

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Q: 3. Solve using any technique y" – 2y/ – 3y = 3e",; 7 ", y(0) = 3, y'(0)

A: We have to solve given problem:

Q: What is the solution of the given equation valid near the origin for x>0? x2y''+x(2+3x)y'-2y=0

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Q: p" +2y' – xy = 0 n(x)= e

A: Given

Q: 5. [10 points] Find the general solution y"-6y' +9y = x*e*

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Q: Solve using any method: y"+y' - 2y = sin x

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Q: y" -2y" - y' + 2y = sin x

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Q: Consider the variable coefficient linear non-homogeneous ODE where and where u and are unknown…

A: The given problem is to find the values of u' and v' for the which the particular solution yp =…

Q: Solve Y" - 6y + 13y = cos(4x)

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Q: 2. Use the variation of parameters to solve: y" -2y" + y' = 4e*.

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Q: b. (1+y²)y" + xy' - 3y = cos x solve and show that this equation is non- linear and non-homogeneous.…

A: As per the question we have to use the solution of the given second order differential equation to…

Q: y = xy' – y* + 1 find general solution and particular solution.

A: Given, We have to find general and particular solution for it. Working:

Q: 5. Solve, using the method of undetermined coefficients: y" + 2y' = 2x + 5 – e-2= %3D

A: First we shall get particular solution of y''+2y'=2x+5. Using method of undetermined coefficients y…

Q: Can you elaborate how to incorporate c into the solution. Like c=0? And how does f'(0)=7 and…

A: Solution below

Q: x.y’ + y + 2y’ – xsinx = 2sinx solve the equation

A: Given that xy'+y+2y'-xsinx=2sinx The equation can be rewritten as, xdydx+y+2dydx-xsinx=2sinx So,…

Q: Q2) Solve: y" - 5y' +6y=H(t-1), y(0) = 0, y'(0) = 1.

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Q: x²y" – 5xy'+9y = 2x

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Q: Find general solution. y" + 4y = 5 sec ² (2+)

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Q: Find the solution of with y(0) = 7 and y'(0) = 6. y" + y − 2y = 54 et

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Q: Find a particular solution to y"+3y'+2 y = x² - 3.

A: Given that,         y"+3y'+2y=x2-3  ⇒D2y+3Dy+2y=x2-3 Where, D=dydx ⇒D2+3D+2y=x2-3  Let, FD=D2+3D+2…

Q: Solve the following initial value problems: (y + 2y - 3y = u(t-1)-u(t-3), y (0) = 0, y'(0) = -1.

A: The initial value problem is given as y''+2y'-3y=u(t-1)-u(t-3) with initial condition y(0)=0,…

Q: Q4- Solve y"- 4y' + 13y 3x.e*

A: Topic:- differential equations

Q: One model for expenditures at high school gives the cosr C, in dollars per pupil, as a function of…

A: The quadratic equation, y=ax2+bx+c can be expressed in the vertex form as y=a(x-h)2+k, where, the…

Q: Find the general solution of the following equation valid near the origin: (1+4x2)y''-8y=0

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Q: step-by-step for y'(1+2y)-2x=0, y(2)=0, and find the interval of validity of the solution clearly.

A: Given differential equation is                  dydx(1+2y)-2x=0      ⟹   (1+2y)dy=2xdx Intergrating…

Q: [  y'''- y' = ex - 2x  ] Please find a particular solution yp for the above.

A: Particular Solution: Consider the equation Let be the differential operator Then equation (1) can…