The general solution to D. E 2y(4) – y'" - 2y" +y' = 0 is given by y(x) = %3D %3D C1 + Cze + Cze+ cje + c2x e + C3e¯* + c4ez* O cie + czez* C3 + C4e* Cje* + c2x e* + Cze* + c4ez* Cie + c2 x e*+

Q: The general solution of (D³+4D)y=0 is (A) Ay=c₁еx+c₂e²x + c3e² (в y=e*(c₁cos2x+c₂sin2x) -4x y =…

A:

Q: 9) =tx-9i Find g8a-16 x-9,Find g9 -16) %3D -16) sa-16

A: Given,

Q: 14. x2 – 2x – 8 <y

A:

Q: - 2. (4)y=x'. D² +5D+

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

Q: 1. y = x* – 2x3 + 5x? – 4, find y*

A: As there are multiple questions, first one is solved here.

Q: Q4: Use undetermined coefficient annihilator approach to solve. y"" – 5y" + 6y' = 10x² – 5x – 6 +…

A:

Q: Laplace transform L{k(t)} = -5{L(t2e-4t)}+L{sin(3t)}

A: We need to find the Laplace transform of the above.                       L{k(t)} =…

Q: Inx+ 1 dy If y = then %3D 2x3 - 3x' will be dx (2x – 3x) + 1) – (In x + 1)(6x² – 3) А. (2x³ – 3x)² -…

A: Use the formula of differentiation of fraction of Two functions in same variable.

Q: Solve the equation (2x + 6) (2y² + 3) dx + 4y(x² + 3x + 2) dy = 0 %3D

A: 2x+62y2+3dx+4yx2+3x+2dy=0

Q: (D 3)²y = e*.. %3D

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: A/If x² (y - 4z) - y²(2x + 3z) + z²(3x - 4y) = xyz Find Zx

A:

Q: Proof. (a) Firstly, from (1), we get 2m+1 < Nm-(7g+6) for n e N, we get that there exist lim…

A: The complete solutions are given below

Q: y-3y" + y' + 5y =

A:

Q: Find the general solution for each of the following equations. 1) (D³-2D² - 3D) y

A:

Q: *29 y-5=m(k-iD= 0(x-1) =O y-5=0 y=5

A:

Q: The general solution of (D-4D)y-0 is (A y=c+ cx + Cze tk ® y-(c, + cx)e* +c3e* © y-c+ cx +Cye" -4x D…

A:

Q: 2y4-6x3 +|1x=-37x-16 dx X3 - 3x2+5x-I5 2x

A:

Q: Solve the equation (x + 2y-4)dx - (2x + y - 5)dy = 0. (x + y - 1)² = c(x-y-3) (x-y-1)² = c(x + y -…

A: x+2y-4dx-2x+y-5dy=0

Q: A triangle has sides with lenaths that are consecutive odd integers. The perimeter of the triangle…

A:

Q: 2. x + y – z = 2   2x + 2y - 2z = ­6  5x + y – 3z = 8

A:

Q: 18. Find the standard form of the equation. 36x + 288x+64y² -768y +576= 0 (x-6)° ¸ (v+4)² _ [A] 1 36…

A: Given equation

Q: -x+y+3z = 3 x+2y-z 0 3x+2y %3D -5z = -2

A:

Q: Find d²y[dx². 1. y = x* - 7 2. y = x + 9 3. y = 2x4 – 5x 4. y = 5x3 + 4x 5. y = 4x2 – 5x + 7 6. y =…

A: The expression d2ydx2 denotes the second derivative of y with respect to x. A polynomial function is…

Q: Differentiate the following expression using the chain rule. 1. y = 10(1+ (2 – (6 + 7x*)°)³)5

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: What is the sum of 7x*+2xy-5y and 2x+3xy+2y7 14x +6x3y2-10y 14x +6xy-10y 9x8+5x3y2-3y 9x*+5xy-3y3

A:

Q: If r2+ 2r –1 = 0 is the characteristic equation of a homogeneous D.E. with constant coefficients,…

A:

Q: 1. (х — Зу + 2)dx + 3(x + 3у — 4)dy %3D 0

A: As per bartleby guidelines we only give first question answers.

Q: 3. 2хydx - (3xу + 2y?)dy %3D0 o (x - 2y)*(2x +y) = c O (x - y)*(x + y) = c (х + 2y)(2x - у)*- с о…

A:

Q: 5. Find the general solution of (D³-D)y=4e*+3ex. Ans. y=2xe*+(1/2)e2+c1+c2e*+c3e*

A:

Q: az Calcula y z = x4 – 2y3 O 8z 4x3 az -6y? O az 4x – 2y dz = 1* – 6y O dz = 4x3 az = 6y? O 8z 4x –…

A:

Q: y²dx + x(x+y) dy=0 A xy²=c(x+2y) B x²y=c(x+2y) © xy²=c(2xy) C D x+y²=c(2xy)

A: Given differential equation  y2 dx +xx+y dy=0

Q: What is the solution of (2x - y)dx + (4x + y– 6) dy = 0? а. (x+у-3)°- с (2х +у- 4)? b. (x-y+3)²=…

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.