The general solution to D. E 2y(4) – y" – 2y" + y' = 0 is given by y(x) = C1 + c2e* + C3e~* + c4e7* Cje* + cze#* - czet* C3 + C4xe* + cje* + c2x e¯*+ Cze" + c4e** C1 + c2e* + + C4e* 2 cje=* + c2e¯³* + C3 + C4e* cje* + c2 x e*+ Cze + C4e* cje* + c2x e* +

Q: 2) Use y = ax to solve 2'y" - xy' + (x+1)y=0.

A: The given differential equation is: 2x2y''-xy'+x+1y=0. We have to solve using y=∑n=0∞anxn+r.

Q: 3) V12-b+4= 6

A: #3 Given,   12-b+4=6

Q: (x- 2)² +(y– 4)² = 9

A: Our Aim is to plot the graph with the help of equation given below:-(x-2)2+(y-4)2=9 -(i)

Q: Verify whether y(x) = 2e-*+xe-* is a solution of y" + 2y + y = 0.

A: Topic = Differential equation

Q: 19. Find the general solution of (D4 + 6D³ +9D²)y = 0. 2 a. y=C₁ +C₂x+C3x² + c4e³x C46 Y = C₁ + C₂x…

A:

Q: nitially 100 milligrams of a radioactive substance was present. After 6 hours the mass had decreased…

A:

Q: Which of the following is the standard equation of 9y² – x² + 2x+ 54y+62

A:

Q: x2 + 2y2 + 3z2 = 1

A:

Q: If f (x) = 4x + 3x2 - 5x +20 and g (a) = 9x - 4x2 + 10x- 55, what is (g-f) (x)? 13x – a2 + 5x – 35 A…

A: See the details solution in below

Q: - 3t -6t + 6' t2-3'-t3 - 4 -6 -6t2 - Let 7(t) = %3D | Find 7 (t) 7' (t) =

A: We have to find the derivative of the vector function

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

A:

Q: Suppose x² y² = x + 17y x = y Find 17 x + y x² + y² + 1

A: Given that, x2=17x+y, y2=x+17y, x≠y Find the value of x2+y2+1. As we know the formula: a2-b2=a-ba+b

Q: 11. In the function y = 3x2 - 3, y is replaced by y and then y is replaced with y +2 ; the new…

A: Given:     Function y=3x2-3   Here y is replaced by 12y       substitute y=12y      12y=3x2-3…

Q: Find the general solution of a = y+2x. O a. y = -z(Inz +c) O b.y = a (2ina +e) O c.y = a(2ina +c) O…

A:

Q: (x²-x) y¹ = (x²+1) y + 12x (x²-1) ³ y' when x = 2, Y = 9

A: Given differential equation is  x3-x y' = x2+1 y  + 12 x x2-13                      ⇒      x3-x…

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: (х? + 2у — 10у3х) if z у? (у? + 4х + 5у) dz -, find || дх

A: Given:

Q: 4. (D2 – 5D + 6)y = 15sinx – 15cosx -

A:

Q: Find the solution. (4D³-3D + 1)y=0 A y = (₁+₂) ²¹/²+c₂e² Get ® By y = (c₁ + ₁₂x) e */2² + c₂e²r x/2…

A:

Q: Given g(x) = 6x – 15x +4x +8x–4 and )= 3x² – 3x – 1, what is the quotient ? A 2x – 17x+10 A 2x-5 B.…

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: Q1: If y" + y = x², then yp = Q4: The solution of y(4) - 5y" + 4y = 0 is: (B) c₁e* + c₂ex +…

A:

Q: Find the general solution to y = c₁e¹¹ + c₂e(8-√³)² + cze(8+√7)₁ Oy=c₁e¹¹ + c₂e³ + c3e-81 Ⓒy=c₁e¹ +…

A:

Q: Find the solution of 4x²y" - 6x²y + y = 0, x > 0 of the form Y₁ = x¹(1+₁x + €₂x² + 3x³ + ...) Enter…

A:

Q: If y=x* - 5x² + 2x – 3 then equals dx A x* - 5x² + 2 В 4x – 10x+ 2x – 34 4x - 10x+ 2x D 4x - 10x+ 2…

A:

Q: Find the general solution of the DEs 1- f"(x)= y"(x)=12x +6x-8

A: The given differential equation is a second order differential equation so we will first reduce its…

Q: 22. (D³ + 7D² + 19D + 13)y = 0 ; y = 0, Dy = 2, D²y = −12 when x = 0

A: see below the answer and calculation

Q: 6. (t -1)+(2 8. (2x² +5xy+ 3y²)+(8x² –7y²)

A: 6.

Q: What is the value of x in (2x - 1) + j(x + y) = (y - 6) + j(2y - 4)?   Answer in rectungalur form

A: We have: 2x-1+jx+y=y-6+j2y-4 Comparing both sides: 2x-1=y-6                  ....(1)x+y=2y-4…

Q: y₁=1+a3x³ + arº +... Y₂ = x + b₁x¹ + b₁x² + ... Enter the first few coefficients: a3 = a6 = b₁ b7 )…

A:

Q: 7. Verify that y = x2 - 1 is a solution of (y')* + y? = -1.

A: Given- y=x2-1 To verify- That the above function is the solution of y'4+y2=-1.

Q: 3(z+9)=

A: 3(z+9)=3z+9×3 By simplify the equation by open the bracket

Q: Which of the following is the general solution of x 2 V) 2 -xy'-56x 2 =0? O a.…

A: We have to solve given problem: Note: given differential equations is wrong. According to options…

Q: 2. (D² + 3D + 2)y= 1+ 3x + x²

A:

Q: -x + y -z = −17 2xy + z = 3x + 2y + z = (x, y, z) =

A: -x+y-z=-17......(1)2x-y+z=24......(2)3x+2y+z=16......(3)

Q: Find C so that y(x)=C(1-x2) a.  y(2)=1 b.  y(1)=2

A: To find the value of C so that y(x)=C(1-x2)...(1) with the given initial conditions.

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.