1 Write step-by-step solutions and justify your answers. (1) Solve the initial-value problem 3" +y-6y = 0, y(0) = -3 and y'(0) 2. (2) ! Solve the boundary-value problem y" + 9y 0, y(0) = -3 and y(m/3) = 2.

Q: he (4x' +6xy' )dx + (9x’y' +3)dy = 0 equation ² - 3x²y' +3y =e - Solve the so *+ 3x°y +3y=e -t…

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Q: Solve y" – 2y' – 3y = 3t² – 5 using the Method of Undetermined Coefficients.

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Q: 5) Use the method of undetermined coefficients to find a solution to y"+y-6y=5Kte-t for a constant…

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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: X1 - x2 +1 = 0) 1. Solve : x,? + x,² = 4 } with seed values x1(0) = 0.8 and x2(0) = 1.8. Compute up…

A: x1 - x2 + 1 = 0  =>  x1 = x2 - 1  x12 + x22 = 4 =>  x2 = (4 - x12)1/2    x1(0) = 0.8, x2(0) =…

Q: (B) Find the general solution of x²y" - (2a-1)xy' + a²y = x²+¹ where a is a constant. Good Luck

A: This question is about ordinary differential equation.

Q: (0-2) dy do With initial value problem // (0) = -1 - 2X - = 3 (8-2) seco tano

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Q: (2) Solve for y in terms of x In (2y+1) + 3x = 1n (4) -1 given

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Q: a) 2xy dx+(1+x²)dy=0 b) y'+(4/x)y=x* ------by exact method ---by linear method

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Q: Solve the following PDES by separation of variable metho (i): u +U, = 0 (ii): y'u, –x’u, = ди (iil)…

A: (i) uxx+uyy=0   ...i solve the PDE using separation  of varaible let u=XxYy differentiate with…

Q: (c) xy' + 4y = 3x², y(2) = 4

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Q: Show that y = 5x2 + 2 is a solution to the DE xy' +(2)/(5) y" = 2y.

A: To show: y=5 x2+2 is a solution of differential equation xy'+25y''=2y

Q: 2x y" +5xy' + y = 3x +2 Answer y(x) = +은+2+

A: The given equation is of the form ax2y''+bxy'+cy=g(x) The solution to the above equation is given by…

Q: 6. Find two solutions to x² - xy - y² = 1 with x,y > 0.

A: SOLVE FOR X   x=4-3y2+y2x=-4-3y2+y2y≤233 ​​

Q: (h) xy" + 8y' +18xy = 0, xo = 1 (i) (3 — x²)y" — 8xy' - 18y = 0, xo = 0 (j) 2y" + 8xy' + 18y = 0, xo…

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Q: 9. (1) Find a second solution of the given equation. t²y" +2ty' - 2y = 0, t > 0, y₁(t) = t. (2) Find…

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Q: Solve ylk + 2) + 2yjk + 1} + v[k] = 0 if y[-1] = 1, y[–2] = 1 %3D

A: Given,                            y[k+2]+2y[k+1]+y[k]=0                               ...(1)…

Q: Find the general solution of x2y" - (2a-1)xy' + a²y = xa+1 where a is a constant.

A: Given  x2y'' - 2a - 1xy + a2y = xa+1  ----------(1)           This is Cauchy's homogeneous…

Q: Ex. (9) Sol:- Solve 3y"-2y'+y= 4x+2

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Q: 1) Find the general solution of the equation x³y"" - 2x2y" - 4xy' + 8y = x² + lnx.

A: In this question we will find the general solution of the differential equations.

Q: 4 Solve y" – y" – y' + y = 2e¬t + te' + 3 by using both the method of undetermined coefficients and…

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Q: (a) y" – 4y" + y' + 6y 0. (b) y" – y" + 2y' = 0.

A: General solution for the Homogeneous differential equations with constant coefficients

Q: 1. Use the variation of parameters method to solve the equation y" + y = secx.

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Q: Solve y"-2y"-5y'+6y=0 general solution y(x) =

A: solution of the given problem is below...

Q: 7 0-3 -9 -2 3 18 0-8 y, y(0) = 2 3

A: Given y'=70-3-9-23180-8y Also given y0=23-1   To reduce to row echelon form and solve for constant…

Q: 1) Find the general solution of the equation x³y" - 2x²y" - 4xy' + 8y = x² + Inx.

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Q: Find the area of the region bounded by the graphs of the functions y=9-x² and y=x+3.

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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: 7. Verify that y = x2 - 1 is a solution of (y')* + y? = -1.

A: Given- y=x2-1 To verify- That the above function is the solution of y'4+y2=-1.

Q: Solve the equation 2 x " y " + 3 x y = (1 + x ) y = ху - which has a regular singula Point x = 0.…

A: Here both p(x)=32xand q(x)=−1+x2x2 aree non analytic at x=0 so 0 is a singular point. But both…

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

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

Q: 5. The function y₁=+1 is a solution of (1-2-2³)+2(1+)/-2yy=0. Find the general solution.

A: PLEASE NOTE: There is a slight  typing mistake in this question ,the differential equation should be…

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: Find general solution y = Yc + Yp of y(3) + y" 3e" + 4x2

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Q: Find the derivative of the function. y = x2e−x

A: Giveny=x2e−x

Q: Find the solution of y" – y – 6y = 48 et with y(0) = 7 and y' (0) = 3.

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