(0) If A"y = has a solution and A -2 0 then O a. a 0.5 O b. a - =-2 O c. a--0.5 O d. a 2

Q: E [X - E ( X)]2 is Select one: O a. V( X) O b. E ( X) O c.E ( X2) O d. S. D(X)

A:

Q: 14. Find y and y" for (a)nie 2* – y4 = 16 ()ao0 nie

A:

Q: Find all a E R for which the given equation does not have a solution: а — 5 7+ 3a 2ах— 5 | - x +1 с…

A: To find: The value of a for which the equation a-5x+1-7+3ax-2=2ax-5x2-x-2 does not have solution.…

Q: dy dr * = 1+ ev-z+5 e + e®+y

A: Option -3:C=x e-5-ex-ydifferentiating w.r.t. x;0=x (0) + e-5(1) +exe-ydydx                -ex-y0…

Q: 2en cos 2t s+ 2 Option 2 None of the choices 2s s2 -2 s2 -2 O Option 5 Option 3 2s s2 +4

A: Given :2eln cos2t

Q: -5 [1 -3 0 and U =0 If y =-1 -141 find the value of x, from Ux = y. 1 Lo 0 14]

A: multiplication of two matrices with the correct size  Option  d is the correct answer  x1= 1

Q: S (20* 2 + - Evaluate 2e* – 2*+2 dx. 2e* – 4, 2* + 2 In x + C In 2 2* + 2 In x + C In 2 В. 2e* – 2-…

A:

Q: 4. y' + y = y?e* ex A. y = С — х e-x В. у%3 С — х ex C. y = С +х e-x y : С +х

A:

Q: Determine E (Y) and V (Y) y -1.0 -2 -0.5 -1 0.5 1 1.0 2 a. E(Y) = -0.63 V(Y) = 1.73 b. None O. E(Y)…

A: Solution

Q: if osta Define fct) = { e²t +etcost if t>"/2 solve y(3)-2y (2) + y² - 24 = f(t) y (0) = 1₂ y ² (0) =…

A: Given differential equation y(3)-2y(2)+y'-2y=ft …………………(1) y(0)=1 ,y'(0)=2, y''(0)=4 f(t)= e2t    if…

Q: In Problem,the graph of a hyperbola is given.Match each graph to its equation.

A: Definition used -                   Horizontal hyperbola -…

Q: -1 So 2/x +¹(xy + 1)dydx 2√x 20 - A - B 40 - C 20 not of above _D ਬ 20

A:

Q: y(r -3)2 dr- 3xe dy 0 4 (x - 3)2 - 18 y+ 18 y e 9 = O e (2 y + 2 y + 1) = c 1/2 3/2 O 4 (x - 3)2 + 9…

A:

Q: The graph of a parabola is given.Match each graph to its equation

A:

Q: 3 - If h(x, y) = y - xy – x2, find at the point (2, n) ду а) - 2.5 b) 7 c) -2 d) -1 e) 0 f) 1 g)…

A: Given that h(x,y)=y-xy-x^2

Q: The nh³ (2x) sech (2x) dx is equal to O A. sech³ (2x) sech³(2x) +C 3 10 O B. tanh°(2x) +C OC. sech³…

A:

Q: If y = ee then y' – y" + e"y' is equal to

A:

Q: 2.25 † Let I" -a" if x + a, f(x) = I-a if x = a, where n e N. Find the value of e that makes f E…

A:

Q: 2 2 Va? +x + Va? -x² If y = Ja? +x? - Va .2 Show that dy 2a 1+ 2 a? dx 3 Va* – x*

A:

Q: If C:7 (1) = (1+t,1-?), -1sts2 and g(x.y)=2xy+x+y+2, then g,(x.y) dx + g,(x.y) dy = a. - 17 Оь. — 18…

A: We have -  g(x,y) = 2xy+x+y+2

Q: olve the following initial value problem (IVP) y" + 2y' – 3y = 3t2 – t + 5, y(0)=0, y'(0) = 0

A:

Q: 12 17 Find p, q if s" f(x) dx + fi2 f(x) dx = " f(x) dx. (Give your answers as whole or exact…

A:

Q: -X If y = cje* + c2e and y(0) = e and y'(0) = 0 then C1 None of These e 1 e

A: Solve it.

Q: -1 Find a) S-4 4(S-3) +16 1 -- b) 8 e StI

A:

Q: 7. If y = e*², then d²y dx2 boins9 (A) (2x)(x² – 1)e*²-2 stod beniu (B) ex2 (C) 2xe*2 (D) (2 +…

A:

Q: d?y Find at t = -1 if x = e' , y = tet dæ? О А. -1 O B. 0 O C. 2 O D. e-1 O E. e

A: Given that: x=et and y=tet

Q: Question 1 S A - -/-/- B If (0 dx (0+2)(x-1)² 12 93 -ja 12 3 - I 3 B -S[ = √( 14+2+ = -1 (1-12 4 +…

A: We can solve this as follows:

Q: 2. fr (x, y) 1/8 1/4 y -1.0 -2 -0.5 -1 0.5 1 1/2 1/8 1.0 2 Find the E (X), E(Y), V(X), and V(Y).

A:

Q: B 2 Show that can be written in the form A + C where A, Band Care T (x - 2)(x + 3) X-2 +3' constants…

A:

Q: 4. Which of the following is a Legendre's equation? a. (1-x²)y" - 2xy' + 3y = 0 b. (1-x²)y" + 2xy' -…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 3. If y x +2 and u = 2x -1 then %3D du a) x b) 1/x c) 2x d) x/2 e) None of the above answers

A: Given that y=x2+2 and u=2x-1To find dydu

Q: Solve y - {x) for x. Then find the input(s) when the output is 2. Ax) = (x- 8)? - 1 O x=t/y+1 +8;…

A:

Q: If y = Eo (k + 1) æ*+3 then y' = E. 00 k=0

A:

Q: 1+ In x If y = 1- In x The value of y' = 10.62 at x = 2 %3D

A:

Q: (,² + 4y² )0.5_x = se!y =r!0in(r) find Ou 2 0.5 when s= 2, r = 4,t = -3

A:

Q: 12.ty′′−(1+t)y′+y=t2e2t,t>0;y1(t)=1+t,y2(t)=et

A:

Q: X1 = 4 Y1 = 2 Y2 = 3 X2 = 2 X3 = 10 X4 = 5 Y3 = 5 Y4 =5 Xs = 7 Ys = 8 1. 3 E-1xi + E=2Yi 2. Σ (y ?.…

A: Note: According to Bartleby guidelines expert solve only one question and maximum 3 subpart of the…

Q: 1 8. The equation of the image when the line y = x + 1 is translated through (3,-1) is? 1 a. y = x +…

A: Please see the below picture for detailed solution.

Q: OX±Y= 0Ý o +Y = ox + oý ±2[ E [XY] – E (X] E (Y] ] |

A:

Q: If A B (C) E +x+ (x-1)(x+1)(x-2) 11 3 - <-2 11 3 None 3 dx = + B +dx, then the value of C is equal…

A:

Q: 5) Solve the Non-linear second ODE: d'y + y? = x2 3x ya

A: Consider the provided question, 3x2yd2ydx2+y2=x2dydx23x2yy''-x2y'2+y2=0yy''-13y'2+13x2y2=0…

Q: =3 ve A2 + A - I = 0 - 1 = 0 , what is det(A+I) I? 1 C) D) 1 1 E) 2 1/4

A:

Q: 3) Solve the following IVP. y" 4y 3(4) (o if te3 gre)=?exr(ase) if tz3 where "exp(x)= e et

A:

Q: If L(1*tet)=y(s), then y(s)=(1/s)*(1/?) a) (s-1) b) -(s-1) c) (s-1)2 d) -(s-1)2 e) s

A:

Q: If e-x, xe-x are the solutions of y''+ay'+by=0 then, y=cx/ex is also a solution of y''+ay'+by=0.…

A: Let us consider the given differential equation y''+py'+qy=0 To solve the differential equation…

Q: 0 if 0 3 Solve the IVP y" + 5y' + 6y =

A:

Q: 4.1+ ež - ) ež + (ež )y' = 0 ex + (ex )y' = 0

A:

Q: (ke) 3 (1-In 2-) 1. For Sk*e3* dx = +C.f u= 3x, then k=? 2.

A:

Q: 1- find y' for y =5x-3/x^2+2x. 2- find y' for y=(1+x-x^2)e^x.

A: 1- find y' for y =5x-3/x^2+2x. 2- find y' for y=(1+x-x^2)e^x.

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.