5. The general solution to D. E 3y(4) – y'" - 12y" + 4y' = 0 is given by y(x) = %3D %3D + cze 3* + C3 + C4e²r cje* + c2ez* + C3 + C4e* C1 + c2e2x + Cze-2* + C4e3* C1 + c2e* + Cze + c4e* cje2* + c2xe2x + Cze-2r + C4e** -2x Cie + Caxe* +

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

A: Given,

Q: 1. y = x* – 2x3 + 5x? – 4, find y*

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

Q: ,3 хуз 1. у' 3 V1+x2

A:

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 given DE x?dy - xydx-2ydx

A:

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

A:

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

A:

Q: 3. Find the general solution of 2ху? + 4 %3D 2(3 — x?у)у'. А. X2у2 + 4х — бу %3D С B. x²y? – 4x – 6y…

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: Find the solution of (2*y² – y) dx + (x²y* – x) dy = 0 o를 +를 - C O 3r°y + 2ry* – Czy = 6 %3D o +를 +금…

A: Please see the answer below

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

A:

Q: If s = (x² + 1)²/3 (3y² + 8y +4) 4(3z+2) 5, find d²s d²s dy² d²s dz²

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: y" + 3y=-48x²e³x

A: Differential equation and it's solution

Q: -2dх 38. y-2dx dy er e2x + 1' УО) %3D 1

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: Solve the DE xy(y² + 1)dx + (x²y² - 2) dy; y(1). = 1 O x^2 (y^2 - 1) = 2 - 4ln(y) O x^2 (y^2 + 1) =…

A: Here we have to solve the differential equation.

Q: dy %3D 1. If x'+ xy-3y' 10, then dx %3D

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: 10-4z .5-2x-y 6z2 dz dy dx

A:

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

A:

Q: 5. 2x+3y 39 y-7 =-2(x+ 10) 3. y = -x + 4 y = -2x – 13 + 13 %3D # y = 3x - 13 3. "y=D- y = * + 2 %3D…

A: Given: 5  2x+3y=396  y-7=-2x+10

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: 1. 4y" — у 3 10 2. (D3 + 2D?)у %3D— 4 3. уМ) — 4y" %3D х — 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.