We consider the initial value problem zy" + 13zy' + 36y = 0, y(1) = 0, y'(1) =-3 By looking for solutions in the form y = z' in an Euler-Cauchy problem Az'y" + Bry' + Cy = 0, we obtain a auxiliary equation Ar? + (B - A)r +C =0 which is the analog of the auxiliary equation in the constant coefficient case. (1) For this problem find the auxiliary equation: = 0 (2) Find the roots of the auxiliary equation: (enter your results as a comma separated list) (3) Find a fundamental set of solutions y1, 2 (enter your results as a comma separated list ) (4) Recall that the complementary solution (i.e., the general solution) is ye = C11 + czy2. Find the unique solution satisfying y(1) = 0, y'(1) = -3

Q: 2) Use y = ax to solve 2'y" - xy' + (x+1)y=0.

A: The given differential equation is: 2x2y''-xy'+x+1y=0. We have to solve using y=∑n=0∞anxn+r.

Q: give me the solution of   y'' - 2y'- 2y = 0

A: Topic:- differential equation

Q: 5) Find the general solution of the following equation y" +8 y"-9 y=0

A:

Q: Example 4: Solve iv) y" – 2y' + y = 3e2x.

A: Given differential equation is, y"-2y'+y=3e2x The auxiliary equation of this differential equation…

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: If y, and y, are solutions of a non-homogenous equation y" + ay' + by = c , then y, - y2 is a…

A: Since y1 and y2 are two solutions of the non-homogeneous equation, we have y1''+ay1'+by1=c…

Q: (2xy² + 2y) + (2x²y + 2x)y' = 0

A:

Q: 1) Find the Solution. a) (y" - 5 y² + 4y = 0 y(0)=4 5) 4'(0) = 0 " 4" "y" + "y' 4(1) = 5 y' (1)=10 +…

A: We have to find the solution of the given differential equation.Note: According to the guidelines we…

Q: Use undetermined coefficients to find the particular solution to y'' - 3y' + 2y = e(-26-24x)

A:

Q: Write down two linearly independent solutions of the Bessel equation 16x?y" + 16ry + (162 – 9) y =…

A: The given differentiate equation can be written as:

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

A:

Q: 1.) y(4) + 4y" + 6y" + 4y' + y = x³e=x

A:

Q: Find the general solution of the following Cauchy-Euler equation x²y" - 2xy' - 2y = 0

A: We have to find the general solution of

Q: 10. y f(x) -2 -2+ a. f(-4) b. f(0) c. f(2) d. f(4) 4, 2.

A:

Q: 5. Find a particular solution to the equation -2x y" + 4y' + 4y = xe¯

A:

Q: Obtain general solution. 1) y''-y=ex-4

A:

Q: 5) Solve y) - 3y4+3y" - 3y" +2y' = 0.

A:

Q: Problem 2 Solve y" - 25 y = x ex

A:

Q: Solve homogenous equation y'''' - 8y''' + 24y'' - 32y' + 16y = 0

A: y''''-8y'''+2y''-32y'+16y=0  operation form   D4y-8D3y+24D2y-32Dy+16y=0  D4-8D3+24D2-32D+16y=0…

Q: Find two fundamental solutions x²y" + 4xy' + (2+x)y= 0,

A: We have to solve given problem:

Q: Solve Cauchi problem x²y" - 4xy' + 4y = 0. y(1) = 0, y'(1) = 1

A:

Q: Find the general solution of the equation y" - 2y' - 3y = 4x −5+ 6xe ²x

A: To obtain the general solution of the nonhomogeneous differential equation y''+pxy'+qxy=gx, use the…

Q: 3 6. Let A = -4 Find the general solution of x' Ах.

A:

Q: oulli’s equation, x' = a(t)x + f (t)x^n, n /= 0, 1, was proposed for solution by James Bernoulli in…

A:

Q: The general solution of y' = X У can be written in the form = C

A:

Q: Solve Cauchi problem x²y" - xy + y = 0. y(1) = 0, y'(1) = 1

A:

Q: Find a particular solution using the Undetermined Coefficients Method of y" -y' + y = 2 sin3x.

A: