Consider at [0, π] the boundary value problem: y''(x) + y(x) = 2x − π, y(0) = y(π) = 0. How many solutions does this have, please give explanation with the steps, thank you in advance

Q: 8. y"-2y-15y=0 y(0)=5, y'(0)=-3

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Q: 3y = /2y – 1, y(1) = 1. ) Find the solution y = y(x) of this IVP. Please present your solution y =…

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Q: y = e"(1 – y²), y(0) =

A: We will find out the required solution for given differential equation.

Q: Find an antiderivative F(x) of the function f(x) = - 2x²5x + 2 such that F(0) = - 15. F(x) = Now,…

A: On solving this we will get

Q: Apply the point-slope formula with x₁ = 3, y₁ = 1, and m = −4. m y-y₁ =3(x-x1) y−(1) = −4[x-(3)]

A: Step 1: Given, Point (x1, y1) = (3, 1), slope = m = -4.we want equation of line by using point -…

Q: At every point of the graph of the function y=f(x) we have y″=12x and at the point (0,5) the tangent…

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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: with y(0) -1

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Q: 4. (6 points) Using separation of variables, solve the differ- ential equation, (1+7)dy dx y Use C…

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Q: ,2k 101. Let F(x) = 2k . k! k=0 (b) Show that y = F(x) is a solution of y" = xy' + y. y(0) = 1,…

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Q: please use the method of variation of parameters to determine the particular solution y'"+30y"…

A: The given differential equation is:y'''+30y''-4000y=e-20x

Q: (c) xy' + 4y = 3x², y(2) = 4

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Q: 6z dy (78)a

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Q: x2y" + xy' – x²y = 0

A: We have to solve second order differential equation Here given differential equation is second order…

Q: 4. Solve x²y" - 5xy' + 8y = 4x², for the boundary conditions y(1) = 1, y'(1) = 1.

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Q: 57) Given: f(x) = ax³ + bx² + cx+d, f(2)=5, ƒ"(1)=-4, ƒ"(4)=12 When x = 1 the tangent line to f(x)…

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Q: { 5) Solve the following IVP y' = t² ((1 + t³) y)−¹, y (0) = yo. of the solution. and find the…

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Q: Solve for x + y (EZ) if i) x² - y² = 24, ii) xy = 35

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Q: Use the reduction of order to find the general solution 21. xy" - y - (x + 1)y= 0, y₁ = e. (0,00).

A: By using method of reduction of order we solve the given ordinary differential equation.

Q: 2) Given f(x) = ax²+bx+c has a y-intercept equal to 5, ƒ"(1)= 16, and (1,11) is a point on the…

A: f(x)=ax2+bx+cy intercept is 5f''(1)=16(1,11) is a point on the curve d dx(xn)=nxn-1

Q: Find the general solution of the equation y" – 2y' + 5y F0 Do not need to show your work, just give…

A: First we find the auxiliary equation and then we find the general solution of the given homogeneous…

Q: Let f (x) = (x³ –- 2x + 2)° Lans(1) = (x' – 2x + 2)' ma g(x) = 5" (x) and 8 (x) = f¯l (x). What is…

A: The slope of the curve g(x) at a point will be the derivative of the function, g'(x) at that point.

Q: xy" + xy² + 4y = /Nx Find the solution y(x)

A: We will find the solution of the differential equations.

Q: Consider the equation y' + 5y = 2. Show that the function o given by: %3D 2 $(x) is a solution,…

A: Given y'+5y=2 We have to find ∅x

Q: y'" If x² + y² = R² (R>0), then K Find K in terms of R. %3D V(1 + (y )² )³

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Q: (b) For the solution that satisfes v(0)1, sketch the solution curve and estmate the following v(0.5)…

A: (b) The solution that satisfies y(0) = 1 can be sketched as follows:

Q: h(x) = px³ + 4px + 1, where p and q are constants. Given that h(-1)=-41 and h'(-1)=67, find the…

A: h( x ) = px3 + 4px + qxh( -1 ) = -41 h'( -1 ) = 67