Find the general solution of the following equation: y" – 6y + 9y = 0 O yG (x) = c1e-3x + c2e¬3x YG (x) = c1e³x + c2xe³x O yG (x) = c1e* + c2e³x O yG (x) = c1e-3* + c2xe-3x = cje O yG (x) = e³x + c2xe³x

Q: Solve the Sturm-Liouville problem 2. Q.7 x*y" + xy'+(16+1)y=0, y(1)=0, y(e" )=0

A: Sturm Liouville problem

Q: 2x 3x The DE whose general solution is given by y = x²+c,e*+C2e is © y" - 5y' + 6y = 6x2 – 10x +2. |…

A:

Q: 11. What is the general solution of (2a-y)dx + (4x +y-6)dy 0 (a + y- 3) = c(2a+y-4)2 (x - y + 3) =…

A: Given differential equation is                                           (2x-y)dx+(4x+y-6)dy=0 let…

Q: 9. Find the particular solution of y" - 2y' + 5y = 0 y(0) = 1 and y'(0) = -2. An

A:

Q: 23. Find the particular solution that satisfies the initial condition. y'+ 3x²y = 3x, Initial…

A: The answer is given below:

Q: 2. Find the general solution of x*v + 1) dx + y'(x - 1) dy = 0 x2 - y? + 2x - 2y + А. 2ln[(y + 1)/(x…

A: No option is matching the final answer. All the given four options are incorrect. The correct answer…

Q: This is the solution of the Cauchy - Euler equation x²y" + 17xy' + 60y = 0 O y = C1x 5 + C2x 8 O y =…

A: Using method of Cauchy's Euler Equation

Q: Get the general solution of the DE (x+2y-4)dx+(2x+y-5)dy=0 a.) (x-y+1)3=C(x-y-3) b.)…

A:

Q: The general solution to y'' - xy' + y = 0 is given by:

A:

Q: 1. Solve ,analytically. the Following differencetegs y(k)+ y(k=)-니3 Ck-2)-4y(e-3).=u(k).…

A: (a) Take the Z-transform on both sides of equation.

Q: The solution of the DE: xy'-4y =x'e* is y =x*e*(x - 1) + cx* O None of these y =x*e*(x+ 1) + cx* y =…

A: First I have convert the given differential equation into linear first order differential equation…

Q: Q. No. 11 The solution of the DE 3ry" + y – y = 0 (a) yı = x³[1 – x + a² + ...], 42 =1+x – 2x² + ...…

A: It is given that

Q: The general solution of (D³+4D)y=0 is Ay=e*(c₁cos2x+c₂sin2x) B y=c₁+c₂cos2x+c3sin2x Ⓒy=c₁еx+c₂e²x +…

A:

Q: If y is a solution of y"+xy'+3y =0 then find the

A: Find y' and y'' from the equation y=∑m=0∞ amxm .                                       y'=∑m=0∞…

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

A:

Q: If y = e2t is a solution to y" – 5y' + ay=0 then a=

A:

Q: Find the general solution of 2xydx + (x^2 - 1)dy = 0. O (x^2)(y) + y = C O (x^2)(y) + y = c O…

A: topic - differential equations if more than one options are correct then 1st and 4th options are…

Q: Find the complete solution of: y" + 4y' + 3y = e with y(0)=1 & y'(0)=0 4.

A:

Q: 2. The particular solution of xyy' = (x² + y²) when x = 1, y = 2 is a. y? = x² ln x2 + 4x² b. y? = x…

A:

Q: Find the general solution of (x³ + xy2 + y)dy + (x²y + y³ + x)dx = 0 %3D xy + In(x² + y²) = c 2xy +…

A:

Q: solve the solution of the Bernoulli's equation 3yły' + - 8(x + 1) = 0; y(0) = 0 x+1

A:

Q: II. Verify if the indicated equation is an explicit or implicit solution of the given DE.…

A:

Q: The general solution of the DE +4-5y=0 dy² y = Ae* + Be5x Option 2 O y = Ae* + Be-5x y= Ae* + Be-5x…

A:

Q: The solution of the initial value problem ydy - xdx 0, y(2) = 0 is y =x +4 y3x -4 None of these y…

A:

Q: Find a particular solution to y" + 6y' + 9y = 3z e

A: We use the method of variation of parameters to find the particular solution to the given…

Q: 2. Verify that e 2 is a solution of the equation y" -3y'+2y=0.

A:

Q: 3. Solve y' = , with initial condition y(1) = 0. y2 – 1 x3

A: It is given that the differential equation dydx=y2-1x3. Using variable and separable method to…

Q: 4 - Find the general solution of y + 3y'+ 2y -e a) y(x) = Cie b) y(x) = Cie 2 + c2e -e c) y(x)= c1e…

A:

Q: The solution of the initial value problem ydy - xdx = 0, y(2) = 0 is None of these y =x² + 4 y=x² +4…

A:

Q: Find the general solution of y) + 3y(4) +y"'' + 3y"= 0. A. y = C1 + C2t + C3 cost + C4 sint + Cse 3t…

A:

Q: The general solution to D. E 2y(4) – y" – 2y" + y' = 0 is given by y(x) = C1 + c2e* + C3e~* + c4e7*…

A:

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…

A:

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: Determine the solution of the IVP y’-2y = 2e^(2x) ; y (0) = 1 a. y = e^(2x)*(2x-1) b. y =…

A: Let's find.

Q: Find the general solution of the DE: y “ – 5y“ + 3y + 9y = 0 יוו -

A:

Q: Find the general solution of x'y + 1) dx + y´(x – 1) dy = 0 2y + 2ln[(y + 1)/(x – 1)] = C 2y +…

A: Given differential equation is   x2(y+1)dx+y2(x-1)dy=0

Q: 5. Find the general solution of yy' + y² = x a.y = x -+Ce-2* b.y² = x ++ Co-* c.y² = x -+ Ce-2r…

A:

Q: 6. Determine the General Solution of this Equation in terms of C y2-x+e2x =DC y+x-e2x C. None of the…

A: To find the general solution of the differential equation in terms of C :            dydx+1xy=xy2

Q: Obtain general solution of the D.E. y + (1/3)y = e'y A) 1/x = e (c - 3x) B 1/y³ = e* (c - 3x) 1/y =…

A: The given equation is Bernoulli equation we will solve this by substitution method

Q: Find the general solution of the following DE. xy² (y')² + y(x - 1)y' - x³ = 0

A:

Q: 4. Find the general solution of (x3 + y³) dx = 3xy² dy = Cx = Cx А. -Зx3 + 2yз В. 7x3 + 2у3 С. -бх3…

A:

Q: Find the general solution of y" + 4y' = 0 O a. y= Ce*+ C2cos(2x)+ C3sin(2x) O b. y= C, + C2e-2x +…

A:

Q: Find the general solution of the DE y" + 4y + 4y = e²x

A:

Q: Find the general solution of the following equation valid near the origin: (1+4x2)y"-8y=0 00…

A:

Q: Find out the optimum solution of the following LPP Max Z= 2X + 5Y

A: Given LPP is Max. Z= 2X + 5Y                                                         subject to…

Q: 2. Find the general solution of x2 (y + 1) dx + y?(x- 1) dy = 0 x2 - y2 + 2x - 2y + A. 2ln[(y +…

A: Given that: x2(y+1)dx+y2(x-1)dy=0

Q: 4. Are y1 (x) = e*and y2(x) = x + 1 solutions of the D.E. xy" – (x + 1)y' +y = x2. Are y1(x)…

A:

Q: Obtain general solution of the D.E. y' + (1/3)y = e%y4

A: