Let y1, Y2 be two independent solutions of (t – 1)y" – ty' + y = 0. If W (y1, Y2)(2) = e² , then W(Yı, Y2)(3) = (A) 2e² (B) 3e (C) e? (D) 2e³ (E) None

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: d) Solve: y"+y"-5y' + 3y = 0

A:

Q: Solve: x'y" - 7xy' + 41y =0

A:

Q: y” – 10y’ + 25y = 30x+3

A:

Q: Verify whether y(x) = 2e-*+xe-* is a solution of y" + 2y + y = 0.

A: Topic = Differential equation

Q: By Lagrange's formula, prove that y =y3-0-3(ys-y- 3) + 0-2 (y_ 3 -y_5).

A:

Q: If y = (x+-) (2x – 3), then dy will be dx a (2x+) + (x = 3)(1 +) G++)(e - x2) + (; ++) = A. (2x +=)…

A: Given that                          y=x+1x2x-3

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

A:

Q: · (D² + 3D + 2)y = xsin 2x

A:

Q: Solve for ‘x’ and ‘y’ where x + y = a – b, ax – by = a2 + b2

A: To solve the equation for x and y.

Q: Solve zx+zzy= 2x, z(0, y) = y

A:

Q: Verify that the function y = c1e (-k+2t)x + c2e (-k-2t)x is a solution to y " + 2ky'+ (k 2 + 4)y =…

A:

Q: DETERMINE SOLUTION OF 1 x dy dx + y = x² + x (2x+3y-13) dx + 3x - 2y) dy = 0 DE

A:

Q: Solve for Y(s) and Y(t)

A: Y(s)=s4−10s3+61s2−360s+9006s3−55s2+217s−1986​ (PLEASE SEE DETAILED INFORMATION ON THE EXPLANATION…

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: What is the special solution of the equation y0̅ ? y''' + 5y'' + 12y' + 8y =5sin2x +10x2 - 3x + 7

A: Find the attachment

Q: Find a general solution of y"=(-2+2isqrt(3))y

A: Given that, the differential equation is- y''=-2+2i3y On simplifying, y''--2+2i3y=0

Q: What is the solution to y' +2 = xy3? * +c a. b. = -x +c c. xy? = - +c d. xy = -x² + c e. None of the…

A:

Q: Solve (1) 5-3x 2. (2) 4. 2 3 y-31 y-5 2 5 (3) 2. 4 4)

A: since we answer only first three sub-parts so we will answer first three. Please resubmit the…

Q: x + 1) ² − 4(x + 1) dx + 4y = 0. Given that y₁ = ²x is a solution; find the general solution. dy dx²…

A: Solution to the differential equation

Q: If y= (x³ + 1)* , then y' = ? A) None of the given choices В 6x²(x³ + 1) O (3x2)2 D D 2(3x²+1) E…

A: Given:- y = (x3+1)2 To find:- y'

Q: 3z2+x 30. If z – xz – y = 0, prove that- =- ax dy (3z²–x)³*

A: Let's find.

Q: Solve 2ry" + (z+1)y+y=0 using y=

A: Series solution of a second order differential equation:

Q: 18. Determine the roots of the auxiliary equation of y" + 3y" – 4y' – 12y = 0 (а) —3, —2,2 (b) -3,…

A:

Q: y= (2x)(3x+1), find y' none of these answers O 6x+2 O 12x+2 O 12x+3

A:

Q: Form the difference equation whose solution is ya = c1 + (c2 + csk)(-1)*, where e1, cz and ca are…

A: Given the solution of the difference equation is           yk=c1+c2+c3k(-1)k

Q: Q2: Solve the following " a) (4D² + 4D + 1)y = 0 b) y"' – 3y" + y' + 5y = 0 - c) y" + y' = x +2

A: Given that  The differential equation is

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.