(D4 − 1)y = 0

Q: Determine  d2y dx2 for y = (4x3 + 8)4.

A:

Q: y = e3x-2y +x² . e 2y

A:

Q: Solve (D-4) x - y = 0 - 6x + (D+1) Y = 0

A:

Q: (D-2D')? z =2x +y

A: In this question f(D,D')=(D-2D')2. To find the solution of the given partial differential equation…

Q: 2(a + 3x) = y - 4x for y

A: Given query is to solve for y.

Q: (D² — 4)y = 8e²x — 12 - -

A: Given; D2-4y=8e2x-12 So, the auxiliary equation is; m2-4=0

Q: (D² + 3D) y = 0

A:

Q: Find Z(D4).

A:

Q: Solve (D3-3D2+3D-1)y=x2.ex

A: The answer is given below:

Q: Solve (D3-3D2+3D-1)y=x2.ex

A:

Q: Find the point on the line 6x + y = 8 that is closest to the point (−4, 1).

A: to find:- point Q(x,y).

Q: dx 4. J、マ-6x+13

A: 4. Given integral:

Q: 4x +2y=O Y=X-3

A: Given ,  4x + 2y = 0  ........... (1)  &  y = x - 3    ......... (2) We have to find x & y…

Q: | (7x + 4) e dx

A:

Q: dx |Vx + 5

A: Explanation: Given that,  ∫xx+5 Let  u=x+5du=12x+5dxdx=2x+5du Now…

Q: Find the point on the line 3x + y = 5 that is closest to the point (−2, 1).

A: To Find the point on the line 3x + y = 5 that is closest to the point (−2, 1).

Q: (x + 2)³ y = (x² – 4) ||

A: a2-b2 =(a-b)(a+b)

Q:

A: Given,       x-x=

Q: 2メy dx +x°dy=o

A: Let's find.

Q: 2. Solve (y + x²y) dy dr = 1

A:

Q: (i) Y = ax + b

A:

Q: X 23 y + 4y = 0

A: Solving second order differential equation:-

Q: (x3-4) 2. S dx x3+2x2+2x

A: To evalaute: I=∫x3-4x3+2x2+2xdx=∫1-2x2+2x+4x3+2x2+2xdx=∫dx-∫2x2+2x+4x3+2x2+2xdx

Q: (2x - y)dx(x + 4y)dy = 0

A: As per the rules, we can answer only the first question and other can be reposted.

Q: (x² D² - xD + 3) y = x²(Inx)4

A:

Q: x-2)3+(y1)3

A: Given: x-23+y13 To simplify the given expression:

Q: (5x+3y = 1 (5x- y = 13

A:

Q: (DE- 6D + 25)у %3D0 y =

A:

Q: x = (1- y)*(3y +1) ;y"

A: Answer is given in next step.

Q: 2. S x²-6x-4 xp x+2

A: Given: I=∫x3-6x-4x+2dx As we know that; The Power rule: ∫xndx=xn+1n+1+C And ∫a·fxdx=a·∫fxdx