by first – shifting find L(e-3t t4) = %3D 24 .a O (6+3)s 0 12 (643)* *9 6. (s+3)4 *0 12 (s+3) 5

Q: 1 dxdy (2x+3y)² 2

A:

Q: Determine yu – 4uzy + a?uzz + 3u = 0 %3D the type of the PDE

A: We will check whether given PDE is hyperbolic, elliptic or parabolic.

Q: dr rVr² +2x – 1 Use the reciprocal substitutionr 1/:

A: The integral is  ∫ dxxx2+2x-1

Q: 1 |(12x5 - 11)dx -1

A: ∫-1112x5-11 dx

Q: хр %3D хр if y = In(7x2 + 6y?). Ap %3D Find seng OM

A:

Q: 7x d.x 2)3 (1 – x²)³

A:

Q: 3x – 5 (ii)! dx. 12x - 7x- 10

A:

Q: Evaluate. Use a capital C for any constant. 14(6z - 1) (62 - 2z - 1)° da %3D |

A: givenI=∫14(6x-1)(6x2-2x-1)9dx substitute 6x2-2x-1=uafter…

Q: Find L{t?e-4t - e-2tsin (v2t)}

A:

Q: x dx Evaluate (4a² +9x?) 2

A:

Q: S₁ y² – 3ydy 11

A:

Q: 3(5+2x) = 45 + 8x

A: We will find the value of x.

Q: Evaluate | x2 Q4. dx + 4x + 3

A: 4) To evaluate the integral

Q: Simplify (ex)3. e(9x + 2) to the form e Ax + B) – eº .ex where %3D 21 B= 2 C = 2 D= 21/2 Xくくく

A: To simplify the following expression

Q: Evaluate L{3e−2(1−t)+t3e2t+2t2sinh(2t)−4e−2tcos(π−3t)}

A:

Q: 26 x 212 = (2*)2 %3D

A: For the given expression it is required to find the value of x.

Q: i= (2,-1) Suppose %3D and Find 3 - 2ui.

A: Given vector

Q: Find the 4** x³ dx А. + c 4 In 4 В. + c 4 In 4 С. + c 3 In 3 D. 24 2 In 2

A:

Q: az Find if yz – In z = x + y ax 3.

A: We have              yz-lnZ=x+y

Q: S(10x* – 2csc?x) dx

A:

Q: Show if z = 2 + 4i satisfies z? – 4z + 20 = 0

A: To show that a value or number satisfies an equation, we substitute the value in the equation and…

Q: dx L. (x² + 1)(x² + 4)(x² + 9)* 8.

A:

Q: B (16x-5) 15x E D What is the m ZFGB?

A: Given figure is : To find the value of m∠FGB .∠FGA=∠CGD16x-5∘=15x∘16x∘-15x∘=5∘x∘=5∘

Q: (1 + 1)e dr 5.

A:

Q: 4a² • 3a5 = (4 + 3)a² + 5 = 7a 7 %3D %3D

A: The solution are as follows

Q: S7=1−1/√2+1/2−12/√2+14−14/√2+1/8.

A: Given:

Q: d 4х +11 15. In((x + 1)(2x + 9)) dx (x + 1)(2x + 9)

A: Given:ddxlnx+12x+9

Q: 8. Evaluate (3x² +6x² – 4x +1)dx.

A:

Q: 5, find m2DEF.

A:

Q: Integrate the given expression. бх — 7 dx 1 A - (6x - 7) 3/2 + c B) none of these 1 C) 을 (6x - 7)…

A:

Q: O Determine the r 2x2 – 3y2 = 38 3x2 + 5y2 = 95 %3D %3D

A: Given :2x2-3y2 = 383x2+5y2 = 95

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.