1 If y = ex , then y equals - 2x A y3 - 2y B 2y D none of the given choices 2x E y3

Q: Find the general solution to the equation xdx + -dy= 3dy O x=/2y+ Cy-2 O xy= 2y + C O y = 2x3 + C…

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Q: Find a particular solution to y" + 8y' + 16y : -7.5e 4t t² +1 Yp =

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Q: A solution to y"-4y'+4y xe+ 2x is O A. y = xe* -2x O B. y = xe" O C. y= e* OD. y= xe 2x * None of…

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Q: If Y(x) = 5x is a particular solution for x'y" + 2y' = h(x) then h(x) = %3D %3D %3D A. 80x* В. 140х*…

A: Given Y(x)=5x4 is particular solution of x2y''+2y'=h(x)....(1)

Q: Let y (x) be the solution of the IVP xy' -3y =x4, y(1)=2 Evaluate y(7).

A: We will rearrange the given differential equation and find a general solution of the given equation…

Q: The solution of the following IVP:y' =y³ x ex, y(0) = 1 Select one: O a. 2-ex2 O b. y=V2-ex2 C. y…

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Q: If y = 3 is a solution to (x – 4)y" – 4y' = 0, x > 4, - then the general solution to this equation…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: What is the general solution of y" + 6y+lly' +6y=0 a y Ge+Gxe + Ge @y=G+Ge* + Ge c. y=Ge*+Ge+Ge…

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Q: y = 2xy – x y = e*C + } In(2y – 1) = –x²+C Option 3 Option 2 In(2y + 1) = -a² + C O Option 4 O None…

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Q: Which of the following is a solution to xy' + y + x*y*e* = 0 ? y3 = x³(3e* + x) y3 = x³(3e* + C) %3D…

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Q: If x, y e R satisfy the equation x2+ y2 -4x-2y+5 0 and S (x + ry) then value of is 100

A: Given : x,y∈ℝ satisfies equation x2+y2-4x-2y+5=0 and S=∑r=099x+ry we want to calculate value of S100…

Q: y = C1e¬ª + C2e¯2# + x y" + 3y – 2x + 2y – 3 = 0 y" – 3y – 2x – 2y+ 3 = 0 - - Option 1 Option 3 y" –…

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Q: The equation y² = cx constitutes an implicit general solution to the DE: Select one: а. 2yy' = x O…

A: The differential equation corresponding to the general solution y2=cx has to be found out.

Q: Which of the following is the solution to y" – 5y' – 24y = 0 %3D a) y = Ae-3x + Be-8x b) y = Ae3x +…

A: To find the correct solution, we will all options one by one (a) y=Ae-3x+Be-8x    →(1)…

Q: y = 2xy – x In(2y – 1) = –a² +C y = e**C + • Option 2 Option 3 In(2y + 1) = –x² + C Option 4 None of…

A: We need to choose correct option.

Q: The particular solution In (x) = 3x + 4y, y(0) = 0 is A. e³x + 3e-4y = 4 B. 4e3x3e-4y = 3 C. 4e3x +…

A: Topic = Differential equation

Q: If y = 4 is a solution to (x- 3)y"-3y' = 0, x > 3, then the general solution to this equation is y =…

A: We have given the second order differential equation. We will use the reduction of order method to…

Q: Find the general solution of 6y"'+y"-15y'=0 3x 5x A y=c,+c,e 2 +Cze -C, 3x 5x B) 2 y=c,e 2 +c,e 3x…

A: Roots are real and distinct.

Q: 19. Find the particular solution of y" + 4y' + 5y = 2e* a. y =e* b.y =e* c. y = -e* d. y =e* 5

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Q: If x = 0; y = -2; y' = 0, find the general and particular solution of 4y" + 25y = 0

A: The given equation is homogeneous differential equation

Q: Find the general solution to y" +(-1) y' + (- 12) y = 5 e2'. %3D a. None b. 7.e2 t y=c, e3t+c, e4t+…

A: To find  The general solution of the given differential equation.

Q: If y= (4x+ 1)(1 –x)°, then y' = ? A (1- x)²(1+8x) B B (1- x)²(1- 16x) -12(1– x)2 C D None of the…

A: Please refer the attached image for complete solution.

Q: 6. S Se(x² + y³)drdy, wherein B = {(x, y) E R²; 1< x² + y² < 4}

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Q: Which of the following is the solution to y" – 5y' – 24y = 0 a) y = Ae-3x + Be-8x b) y = Ae3x + Be8x…

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Q: The general solution of y" + 4y' + 4y = 2t +3 is: Select one: а. y = Cq e-2t + C2 t e-21 + 2t +3 b.…

A: The solution is given as

Q: If y = ex , then y equals A none of the given choices - 2x - 2y x3 2x D 2y E x-

A: Let's find.

Q: The solution of ry-y-2r', y(1)-4 is (A) y= a+2z (B) y-z+4zr (C) y =z + 3r (D) y= +3z (E) y-3z+ 1

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Q: Evaluateſ 2y³ e>ʻ. a. ey²y² – 1) + C b. -ev*y² + 2) + C c. 2ev*(y² + 1) + C d. ev*y + 2) + C 2e»*(y?…

A: Given: I=∫2y3ey2dy=2∫y3ey2dy     ....1 Let, t=y2So,dtdy=ddyy2dtdy=2yydy=dt2 Now substitute these…

Q: Find a particular solution to y" + 5y + 4y = -10te". Yp =

A: Given the D.E. y''+5y'+4y = -10te3t We have to find particular solution yp of this equation.

Q: The general solution to D. E 2y(4) – y'" - 2y" +y' = 0 is given by y(x) = %3D %3D C1 + Cze + Cze+…

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Q: 19. Find the particular solution of y" + 4y' + 5y = 2e* a. y ==e* b. y = c. y = -e* d. y = e* 5 O A…

A: To find out the particular solution.

Q: If y = e* , theny equals – 2y A x3 - 2x B 2y 2x D y3 E none of the given choices

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Q: Give the general solution to y"- 2y'-8y =0 a) O y=C, e"+ C, e* b) O y=C, e* + C, e* -2x 4x c) -4x +…

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Q: The general solution of y" + 4y' + 4y= 2t + 3 is: Select one: а. y = Cq e-21 + C2 e-21+2t +3 O . y =…

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Q: Find the general solution of 6y''+y"-15y'=0_ 3x 5x y=c,x+Cge 2 2 +cze 3x 5x 2 2 B y=c,+cze ? +cze 3x…

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Q: Find a particular solution to y"+6y +9y = 5e-3t t2 +1 Yp=

A:

Q: Find a particular solution to y" + 6/ + 9y = 3.5e 3. Yp =

A: Given thay  y"+6y'+9y=3.5e^(-3t) To fin the particular solution

Q: If y is the solution of the I.V.P f y" -4 ty' +6 y = 0, y(1)=6, y'(1)= 6, then y(2)=32. Select one:…

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Q: If y = ex, then y equals 2x (A - 2y В +3 C) none of the given choices - 2x D E

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Q: Find the general solution of y'=x-2y O 4y=2x-1+Ce^-2x O 2(x+2)^-1 + c(x+2)^-4 x=y^2 -1+Ce^(-y^2) O…

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Q: Find the solution. y' = 5y + e-2x y-2, y(0) = 2 -15x 13e A) y = + 3e 2r1/3 23 139e 15x – 3e -2x \1/3…

A: Given differential equation is in the form of Bernoulli's differential equation.

Q: Find the particular solution of y" - 2y +y=D0, y(0) = 5,y(0) = 1. O a. y= 5ex – 2xe* O b. y= 5e-x –…

A: We have to find the solution

Q: 1 If y = ex , then y equals (A none of the given choices – 2y B) x3 2y x3 - 2x y3 2x E) y3

A: To find y'

Q: The general solution of the DE: y" – 3y = 0 is Select one: y = ce² + cze³z y = c +cze³z y = ce² +…

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Q: If y = f(x) is the solution of y" – 9y" +26y' – 24y = 0, f(0) = 4, f'(0) = 15, f" (0) = 44, then

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Q: If y is the solution of the I.V.P t y"–4 t y' +6 y =0, y(1)=7, y'(1)=4, then y(2)=15. Select one: O…

A: We have to solve given initial value problem

Q: The solution of y" – 4y' + 4y = 0 is Select one: O a. y = cje2z + c2e¬2 O b. y = c1re2= + c2xe³z O…

A: The given equation is y''-4y'+4y=0

Q: If y = ex , then y' equals (A none of the given choices - 2y x3 2x 2y D 2x E

A: Please refer the attached image for complete solution. THANK YOU.

Q: 2) Find the general solution. y" + 3y" – 4y' – 12y = 0 d°x d*x d³x 12 ds d²x ds ds²

A: Here we calculate roots of auxiliary equation.