determine the roots of the indicial equa- tion of the given differential equation. Also obtain the general form of two linearly independent solutions to the differen- tial equation on an interval (0, R). Finally, if r1 -r2 equals a positive integer, obtain the recurrence relation and determine whether the constant A in y2(x) = Ayı (x) In x +x2 bnx" n=0 is zero or nonzero.

Q: Fin 7-√42 X mZX = Y O 21/14 N

A:

Q: Find y′′, if y=x√1+x2.

A:

Q: (3 + j4) (1-j) E. If x+jy find x. 4-j5 a. -0.005 b. -0.125 c. -0.454 d. -0.951

A: we know that: j2=11j=-j(a+b)(a-b)=a2-b2

Q: If z = x² - xy + 3y2 and (x, y) changes from (3,-1) to (2.96,-0.95), compare the values of Az and…

A:

Q: (D³ – 3D + 2)y = -7 5.

A: Solve the following

Q: Determine d2y dx2 , if 2x3 − 3y2 + 7xy = 0

A: We can make it easier for you

Q: 4=6xt -11 t.

A:

Q: dx 19. Evaluate using substitution f V5-4x-2x2

A: I have used method of substitutions

Q: C.CC-3yz)dxdydz n=2 2. Evaluate

A:

Q: (5) Given z=x³y-3y². If x changes from 2 to 1.9 while y changes from 1 to 1.02, find dz and Az. Is…

A: The objective of this question is to find the change in z (dz) and the approximate change in z (Δz)…

Q: Answer 6. Solve (2y² +2y+4x²)dx+(2xy+x)dy=0 6. C=x°y* +x*y+x

A: Given differential equation  2y2+2y+4x2dx+2xy+xdy=0.....1 Compare equation (1) with Mdx+Ndy=0, we…

Q: 1 Q 2. Differentiate h(x) = (V+ -2 IX

A: The equation can be re written as,

Q: Find (e3x + 5sinx)dx. -e3x +5cosx +C O a. 3 e3x+1 -5cosx + C b. 3x + 1 e3x -5 cosx + C OC. -e3x -…

A:

Q: (1) Evaluate the iterated integral by converting to polar coordinates. 2√2x-x2 x² + y² dy dx

A: A given integral We have to integrate it by converting it in polar coordinates

Q: dy 6. dr = (2 +y + 1)2

A: The given problem is to solve the given ordinary differential equation, we can solve by using…

Q: 5x-y2 2xy+3y2" c. xy? - 2x5 + 3y³ = C d. xy? + x5 + y3 = C 29. Find the general solution in implicit…

A: We have to find solution of exact differential equation.

Q: 2xy Simplify 3z2 a. 6x³ y6 9z5 O b. 8x3 y° 27z6 C. 8x3 y° 27z5

A: Given: simplify 2xy33z23 We know that amn=am×n                                             ..1

Q: 2. Find P.S. of when y (2x²-xy +y ²) dx − x²(2x-1) dy o y = 1/2. X = /

A:

Q: The tanh (2x) sech (2x) dx is equal to sech (2x) sech (2x) +C OA 3 10 OB. sech (2x) sech (2x) +C. 3…

A: Solution

Q: 1 1+x2 (y + 2x)¯i dy dæl 0 0

A: Double integral

Q: 10. (D² – 3D) y= 9x² = 9x2

A: 10) Given Information: Given differential equation is D2-3Dy = 9x2

Q: Solve for the value of C in the equation: (3xy2 + 2y)dx + (2x²y + x)dy = 0 when y(1) = 2 O A. 4 B.…

A:

Q: J(2m-a)(√m² - am - a² dm

A: The given integral ∫2m-am2-am-a2dm. We have to find the integral value.

Q: Find the solution of the Bernoulli's equation + = y3(1+ In x). dx a. 9 = -6xy?(1+ In x) + 2xy? +…

A:

Q: Evaluate. 9 -4 I| (6x + y) dx dy 0 -5

A: Integration is a process of finding the anti derivative of a function. There are basically two types…

Q: 4.a) Find d dx y = ln (2²/ n (²x + 5) b) Find dy dx y = 3√√x++2x e³x (5x²)

A:

Q: 2. y(4) + 2y" = 2 А. 2х В. 1 C. ½x? D. x?

A: here we need to find the particular solution of given differential equation. the solution is…

Q: 9 = dy

A:

Q: x° +2 y=- e3x +9

A: Given: As x→∞, y=x6+2e3x+9 To find: limx→∞x6+2e3x+9

Q: dx 43. Evalua Jx +2)(x² +4x + 10) te

A: To simplify this integral, we use partial fraction decomposition. Thus,…

Q: d²x is dy2 15 If x = (3 2y)5/2 , then 15 А. — A. -15(3 - 2y)1/2 В. 2 (3 2y)1/2 C. - (3 2y)1/2 D.…

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.