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: dy = 2y and the solution to this equation includes the point (-1, 1), then y = dx 5. , Given (A) e²r…

A: Given : dy/dx= 2y includes point (-1, 1)

Q: What is the general solution of xy(xy³ – 1)dx + x²(1+xy)dy=0? A 2x°y³ -3x²= Cx² 4x³y? +3x?= Cy ©…

A:

Q: - 2. (4)y=x'. D² +5D+

A: Given differential equation is, D2+5D+4y=x2.

Q: x²y" + 2xy' – 2y = 0; x > 0; y = y(x) (1) 3. Determine if the two solutions in Questions 1 and 2 are…

A: The general form of a second-order homogenous linear differential equation is given by…

Q: If (1 – i) x + (1 + i) y = 1 - 3i, then (x, y) =

A:

Q: Q5. Use the method of undetermined coefficients to solve (a) y" + 2y + y = x²e-". (b) у" — 2у + 5у 3…

A:

Q: let h(y)=(y-3y2)5(y2+2)6  h'(y) in simplified form.

A:

Q: 9) Solve: (x + y)dy-(z-y)dx=0 a) x² + y² = C b) z² + 2xy + y² = C c) z²-2ry+y²=C d) z²-2ry-y²=C

A: We need to solve D.E.

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: 8.) y" +2y' +5y = 3e 2* ; and y(0) = y'(0) = 1

A:

Q: Solve the nonlinear ODE Ay''+Byy''-y=0, where y=y(x) and A,B are constant

A: The given nonlinear ODE is: Ay"+Byy'-y=0 where y=yx and A,B are constants.

Q: ye x, (21x) satisfie s Show that the equation

A: Given: The given equation is xy''+n+1y'+y=0  ,  y=xn22x

Q: (C) y" + 21y+8x=y" + 5y' + e²*

A:

Q: Let y1, Y2 be two independent solutions of (t 1)y"- ty' +y = 0. If W(y1, Y2)(2) = e2, then W(y1,…

A:

Q: If y = v3x , then y' is A. -1/2 B. V3 x -1/2 С. /3x V3 D. 2 V3 -1/2

A: Given y=3x

Q: Are the functions y₁(x) = e, y2(x) = ze a fundamental set of solutions for the equation y" - 2y + y…

A:

Q: Let y be the solution of y'+y=x, xER,y(-1)=0. Then, y(1) 류를 ²-28² 2-2e -

A: Since given that y be a solution of differential equation…

Q: Consider the second order differential equation y" - 5y' + 6y = 0, y(0) = y'(0) = 1 Then y(t) =

A:

Q: У). y), where

A:

Q: (Зху — 4у — 1)dx + x(x — 2)dy 3D 0; when x — 1,у %3D 2

A: According to  given Bartley guidelines to solve only one question at a time if it is not mentioned…

Q: ) Verify that y=e-2x is a solution of equation x(y")3+ (y')4 – y = 0

A:

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: 2a) find a solution of y" (x) = y(x) that passes the origin and go trhout the point (In(2),-).

A:

Q: =² + 2y²) = ry, y(-1) = 1 dy O 2n* = y² + a? O a* = 4 (y² + a²) O a4 = 2 (y² + x²)

A:

Q: b) y(4) + y(3) – 7y(2) – y' + 6y = 0. c) y(4) – y(3) – 7y(2) + y' + 6y = 0.

A: Solve the given differential equation Here I am giving answer of 1 st problem if you want answer of…

Q: Consider the equation y" + ay' + by = f(x) the constants a and b are real and different from zero,…

A:

Q: y=cJ,(/2x) +c,J,(/2x)is solution for x?y "+xy'+ (2x² – 4) y=0

A: Given, y=C1J42x+C2J42x is solution for x2y''+xy'+2x2-4=0 To find that this statement is true of…

Q: 11. Solve: 2xyy'= x² y° +4y² a. 8x' = y(C – x*) b. 8r = y (C – x*) c. x² = y(C – 8x*) d. 8x = y*(C…

A:

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:

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.