A B 4. n(A UB) = 155 n(ANB) = 30 n(B) = 105 30 Solution: y O x = 20,y 30 O x = 30, y = 75 O x = 50, y = 75 O x = 80 m y = 75

Q: 4. Obtain the general solution. y"-4y'+4 y=3e²*

A: for the solution we have equation y" - 4y' + 4y = 3e2x so now characteristic equation of this is...…

Q: r4 & 2Vz& /4z=x? 2. JJJO & 0 & 0 Jo & 0 & 0 S dydxdz

A:

Q: 8. What is the particular solution of 2xyy' =1+ y², when x = 2, y = 3 ? C. y =V5x +2 d. y =3x – 4 a.…

A: Given differential equation 2xyy'=1+y2, when x=2,y=3. The objective is to find the particular…

Q: (D^4 + 3D^3 + 2D^2)? = 0

A:

Q: Find the general solution  (D2 − 2D − 3)y = 0 when x = 0, y = 0, y′ = −4

A: The given equation is,D2-2D-3y=0with the initial condition,x=0, y=0, y'=-4

Q: Find the general solution. 1. (D2 + 3D − 18)y = 0

A:

Q: Solve the equation 18y – 17 = 7 for y. O A) 2 O B) - 4 3. 4 O D) 5. 3. 4-

A:

Q: he solution of the IVP y" - 3y' - 4y = 0, y(0) = 0, y'(0) =5 is: Select one: O a. y = e4t - e- O b.…

A:

Q: What is the general solution to 3yy' – x² = 0 for æ > 0? O y = a3 + C2 O y = '음교3 + C2 9. O y = /žæ³…

A: using variable separation method,

Q: y? + 3xy Solve the IVP y' y(1) = 5 using appropriate substitution. x2

A:

Q: 4 Solve for the general Solution : 3x²ydx + (y* – x³)dy – 0 Select the correct response: ,3 4. O x°…

A:

Q: Show that y = 5x2 + 2 is a solution to the DE xy' +(2)/(5) y" = 2y.

A: To show: y=5 x2+2 is a solution of differential equation xy'+25y''=2y

Q: y Sx-4 y 5x-5 no solutions b. a. one solution

A:

Q: Determine whether y(x) = 2e-* + xe-* is a solution of y" + 2y' + y = 0. Is y(x) = 1 a solution of y"…

A:

Q: Find the number of positive integer solutions (x, y, z, w, t) to the equation 2x + 3y + 4z + 3w + 2t…

A: Find the number of positive integer solutions x,y,z,w,t to theequation 2x+3y+4z+3w+2t=20?

Q: Find the solution of y" + 6y + 9y = 150 e² with y(0) = 7 and y' (0) = 9.

A:

Q: Solve second order DE y" - 4y' + 4 = 0

A:

Q: ds dS S 2. Find the solution 2 -= 5t³S³ dt t

A: Let's find.

Q: 32 + ar – 10x - br + c (r - 1)(r+2)2

A:

Q: How do I solve q=f(t)=t3/4+t2/3+6 if t=4?

A: Given function and value of t are,

Q: (3x²2y²)y' = 2xy,when x = 0, y = -1

A:

Q: 3. Find the number of non negative solutions to x +y + z + w = 21.

A:

Q: 5. Find the Solution: y" + 2y' + y = cost y π y (²₁7) = 1 y' y'(-7)= = 2

A: Given that y''+2y'+y=cos t To solve the given differential equation.

Q: B) Use ers to nnd the general solution y and the partic Ур- e 26. y"+ 2y' +y V1 – x² II

A:

Q: Q3. Verify that y² = x² – 3 is the particular solution to the following ivp: y' = ; y(2) = -1. %3D

A: To check whether a solution is particular solution to ivp , it must satisfy the differential…

Q: 2. -4 y= 글x + 1 y = + 6 m = m = 23 4 5 주. . t. 5. 9. b = b = SOLUTION:

A: The equation of a line is given by y=mx+c in one form. The other form of a line is given by ax+by=c.…

Q: Now gx y"_y₁-2y=C₁e +4c₂e² २०७ +4₁e - alge 20₁0 x 2c2e

A:

Q: Obtain the general solution: 1. (D² + 6D + 9)y = 18e 3* -3x

A:

Q: (D² + 4D + 4)y=0 when x = 0, y = 1 and y = -1

A:

Q: A. Obtained the general solution. 1. (D2 – 6D +9)y = e*

A: In this question we have to find the general solution.

Q: Q10) The general solution of y+2y"-y-2y = 0, is: a) y(x) =ce²+₂*+* b) y(x) = c₂e-+6₂8 Q11) L(y") =

A: Solution :-

Q: Q(4) Find the general solution of dy =(r- y+ 5). dr

A:

Q: What is the solution of the DE: x²dy + y²dx = 0? A. x+y = cxy C. -=c x y B. D. None of A, B, or C -…

A:

Q: Solve for u = u(x, y). Uyy + 10uy + 4lu = 5e5y. NOTE: Express the answer in terms of c1(x) and…

A:

Q: Find the particular solution: y" + 16y' = 0, when x = 0, y = 0, y' = 0, y" = 1

A:

Q: 8. What is the particular solution of 2xyy' =1+y², when x = 2, y = 3 ? а. у%3D5x -1 C. y =V5x + 2 b.…

A:

Q: S 2x + y = 0 | 3x – 4y = – 19 2 I| O Yes, this is the solution. O No, this is not the solution.

A:

Q: What is a solution of the first order equation Y (K+1) = Y(K) +5 ? Ans: y(K) = 20+5k

A:

Q: 3 By using the first principles, differentiate (x)= 3 S'(x) = %3D Answer: 2x2

A:

Q: Find Particular solution only 3 y" - 2y" + 12 y' – 8 y = te %3D

A: We need to find particular solutions.

Q: Obtain the general solution. (D^3 - 4D)y = 0 when x = 0, y = 0, y' = 0, y'' = 2

A:

Q: Solve the IVP: y" + y' = 0 y(n) = 0, y'(1) = 2, y'"(n) = -1

A:

Q: What is the solution of 2r (y + 1) dr ydy 0 when z = 2 and y= 0 ? In(y +1) + 4 1- In(y+1) +3 In(y+1)…

A:

Q: Solve the IVP: ty" - ty' + y = 2+u₁(t)8(t-2), y(0)=2, y'(0) = −4.

A: Introduction: When an initial value problem is provided, we use Laplace transformation. This method…

Q: y" + 10y + 25y: 18e-5t t2 + 1 Yp =

A: Given : y" + 10y' + 25y = 18e-5t/(t²+1)

Q: III. Obtain the general solution: 1. (D² + 6D + 9)y = 18e 3* -3x

A:

Q: 2) solve the IVP: (here=d 2 2++4 y ² - 4y + 4y = { [0" 2t -C +9 osts2 +32 y(0) = 4,4 (0) = -1

A: Given initial value problem y''-4y'+4y=e2t+40⩽t<2-e2t+4t⩾2,y(0)=4,y'(0)=-1. The objective is to…

Q: 3) xle), ale), zl4) genecal solutions? 3x+G4-22 %3D - 2y

A:

Q: 2) Gr. Find a solution for the BVP: y" + 49y = 0, y'(0) = -3 and y') = 3. %3D

A: