A projectile is fired vertically upward and has a position given by s(t) = - 16t + 288t + 304 for 0sts 19.

Q: Q6. Find general solution of the DE 4x²y" + 8xy' + y = 0

A: This is Cauchy- Euler equation. We can solve this equation as follows :

Q: Q2 Find the general solution of y" + 5y' +6y = 4e +5sin .x.

A:

Q: Find the general solution of the following: 11.(D² – 2D + 5)y = 0

A:

Q: x²yy' = eY (FINAL answers should be in terms of C)

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 a particular solution to y" + 4y' + 3y = -16te²".

A:

Q: Solve the d.e. using Method of Undetermined Coefficients (MUC) (D² – 3D – 4)y = 30e4x ||

A:

Q: Q1. Verify that y= is a solution of the DE -20t y + 20y = 24 %3D

A:

Q: d²y 54. Let y = 4r+2r+l_find CL)

A: To find the double derivative of below expression.

Q: Consider (D3 + 3D² + 2D)y = 3x2 + 5x + 9. Using method of coefficients, what is y A y = 6x – x2 + 2…

A:

Q: The position of a particle is given by s(t) 2t3- 12t2 +18t, %3D is in seconds.

A:

Q: Use the method of reduction of order to find a second solution to ty''−(6t+4)y'+(9t+12)y=0,  t>0…

A:

Q: Solve the equation using Reduction of Order (D² - 5D + 6) y = 2e* Oy=e+c₁e²x + 2c₂e³x Oy = √² + ₁³x…

A:

Q: f(x,y) = 40x+ + 72x³y+ 85XU fur eblidl w jall dissui %3D -226x2 A O -226 BO 216x2 CO

A: To find fyx = ?   Given : f(x,y) = 40x4 + 72x3y + 85x

Q: D={(x,y):4 < x² +y² < 81,< x <-V3y}, V3 Find [S, dA JJp y2

A: We will use polar co ordinates to solve the problem

Q: -(D² – 25) y = x e* . Using method of undetermined coefficients, what is y Consider A ' = Ax e* + B…

A:

Q: The y, of (D²+D)y=11 .A e¯X+11 .B 11 .C 11x .D does not exist

A: Given that  (D^2+D)y=11  To find the particular solution differential equation

Q: Q2. Find of y = 4x/x + v at x=1? dr

A: We have to find the dydx of y=4xx+x at x=1.

Q: Solve the DE using the method of variation of parameters: x²y" – 4xy' + 6y =30x³, y(1) =5 , y’(1) =5

A: homogeneous system is  compare this equation with  so here we have

Q: Use the method of undetermined coefficients to find the general solution y'' +3y' +2y =e-t +t2 +2t

A:

Q: Use undetermined coefficients to find the particular solution to y'' + 2y' – 4y = 2t + 2 Yp(t) =

A:

Q: Show that п-2 Ag:1 = E :uk+'4æ + v"n-1Px• k=0

A: Given  Ax:n=∑k=0n-2vk+1qxk\+vnpxn-1

Q: The cost per day to society of an epidemic is C(x, y) = 40x + 230y where C is in dollars, x is the…

A:

Q: Use undetermined coefficients to find the particular solution to y'' – 7y' + 10y = 3e-2t Y(t) =

A:

Q: Use undetermined coefficients to find the particular solution to y''+ 7y' + 10y = 3e Y(t) =

A:

Q: Find a general solution. 7y" + 13y' - 2y = 0 y(t) =

A: Solution

Q: 6. x = t and y = 3t – 2 for 0Sts4 %3D -

A:

Q: Q1: using variation of parameters to solve: * y"' – 2y" – 21y' – 18y = 3 + 4e-t %3D

A:

Q: Use variation of parameters to pind Yr F -2xy' +ay: -12 x) given that = x and Yx art solutions of…

A: Let's find.

Q: Find the solution. dy 3+9y =2ty53 (A) y- 3er - 3 (B © y - 34-3e2

A: To solve the given differential equation first we will arrange the differential equation in the form…

Q: Q6 Find dy, if y- +++

A: Given :y=xxx

Q: Use the method of reduction of order to find a second solution to ty’ – (8t – 3)y' + (16t – 12)y =…

A: Given: ty''-(8t-3)y'+(16t-12)y=0, t&gt;0y1(t)=e4ty2(t)=? We have to find the second solution y2(t)…

Q: Q6. Find general solution of the DE 4x²y" + 8ry' + y = 0

A: We need to find the general solution of the given differential equation. The general solution of the…

Q: Use undetermined coefficients to find the particular solution to y'' + 4y' – y = 5t° + 5t + 8 -…

A:

Q: Find the general solution by substitution or elimination Q6 A: * = x -2 y +t — х —у+2t dt

A: The system is x'y'=1-21-1xy+t2t Obtain the eigenvalues: A-λI=01-λ-21-1-λ=0-1-λ2+2=0λ=±i The solution…

Q: Is the equation t²y' (1) t + 4 - separable? y?

A: t2y't=t+4y2

Q: Use the method of undetermined coefficients to find a particular solution to y'' – 9y' + 20y = 3et…

A:

Q: Solve the given DE using the method of undetermined coefficients. (D² + 3D+2) y = 12x2

A: Let's find.

Q: The population of a colony of squirrels is given by 1500 p(t) %3D 3 + 2e-0.1t

A:

Q: dz Find from the equation x*y+ x z+ z² = 4 ax

A: We differentiate both sides with respect to x, considering z is a function of x.

Q: Find the general Solution of the diff. equ- x*y" +zxy-2y=D0 ?

A:

Q: y" – 7y' + 10y = 4e" + 3e2". |

A: The general solution by undetermiend coefficients is given as follows :

Q: Use the method of undetermined coefficients to find the particular solution y, y" – 4y" + 4y' = 2x –…

A:

Q: Find the general solution to the DE y"-6y'+9y=t2e3t

A:

Q: Q5/ Find by using chain rule dx y = vt - 5 +t, x = tV4t + 8 +7 %3!

A:

Q: Given that y1 = x² is a solution of the equation r²y" – 3ry'+4y = 0 on (0, oc), use reduction of or…

A:

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

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

Q: The owner of a video store has determined that the cost C, in dollars, of operating the store is…

A: topic- application of derivatives

Q: Q3) Find fog(x), gof(x), D, D fog' gof x+2e f(x) = » g(x) = vx – 2 %3D 2

A: Solution:-