Find the solution of the given initial value problem 98y" + 21y"+y = 0, y(0) = -8, y'(0) = -14, y'"(0) = 0. y″(0) On paper, sketch the graph of the solution. How does the solution behave as t→∞? y(t) As t = → ∞, y(t) - →>>

Q: Find a general solution to the following higher-order equations. (a) y'' - 5y'' +6y' +12y=0 (b)…

A: The given differential equations, a) y'''-5y''+6y'+12y=0 b) y'''+3y''+y'-5y=0 c) y'v+13y''+36y=0 We…

Q: Find the general solution y''-y'-2y=0

A: Given the differential equation y''-y'-2y=0. We need to find the general solution of the above…

Q: The general solution of y' = 10 can be written in the form Y =C D

A: We are solving the given problem by using the method of separation of variable.

Q: 2.- Find the solution of the initial value problem: y + ycost =D 극 sin 21, y(0) = 1

A:

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: Is (y − 33)2 = 4a(x − h) the solution to the diff. equation (y-33)y''+(y')2 =0

A: soln:Giveny-332=4ax-hdifferential equationy-33y''+y'2=0

Q: 6. Solve by Frobenius method (in power of a): 2x²y" + xy' + (x² - 1)y = 0.

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Q: 3. Find the complete solution of: y" - y' + y = 1 with y(0)=a & y'(0)=ß

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Q: Solve the following Bernoulli equation y' – y = (2t – 3)y i

A: Bernoulli Equation : Consider y'+p(x) y=q(x)ynThen we let v=y1-nAnd solve the equation by…

Q: (d) Solve the y" + 4y' + 3y = 0, with y(0) = 1, y'(1) = 0

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Q: Find a solution: ty''-ty'+y=2; y(0)=2,y'(0)=-1

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Q: - 4. 3y(x² − 1)dx + (x³ + 8y − 3x)dy = 0; when x = 0, y = 1

A: