Suppose ay" + by' + cy = 0 with y(0) = d and y'(0) = k has a general solution y = 4e2 3. What are the constants a, b, c, d, and k?

Q: he (4x' +6xy' )dx + (9x’y' +3)dy = 0 equation ² - 3x²y' +3y =e - Solve the so *+ 3x°y +3y=e -t…

A:

Q: 8. y"-2y-15y=0 y(0)=5, y'(0)=-3

A:

Q: Solve 2y'' - 5y' - 25y = 0, y(0) = 0, y’(0) = = y(t) = - 37.5

A:

Q: show that y=x2 is one of this equation solutions x2y''-2y=0

A:

Q: Use undetermined coefficients to find the particular solution to y'' - 3y' + 2y = e(-26-24x)

A:

Q: Obtain the particular solution for the equation 2(x³ + 7)y' = x?y when x = 1, y = 4.

A:

Q: 2- y'" + 7.5y" + 14. 25y' – 9.125y = 0, y(0) = 10.05, y'(0) = -54.975, y"(0) = 257.5125 %3D %3D…

A: As per answering guidelines of Bartleby I am supposed to answer only first question. If you want…

Q: a) 2xy dx+(1+x²)dy=0 b) y'+(4/x)y=x* ------by exact method ---by linear method

A:

Q: please use the method of variation of parameters to determine the particular solution y'"+30y"…

A: The given differential equation is:y'''+30y''-4000y=e-20x

Q: 1. y = 3x? – 2x4 - 3x3 + − − 2x + 1; y(4) - 8

A:

Q: d'y (3x-5)(2x + +9x=6) Determine the and of y = 7x Solution:

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: 5. [10 points] Find the general solution y"-6y' +9y = x*e*

A:

Q: Suppose ay″+by′+cy=0 with y(0)=d and y′(0)=k has a general solution y=5e^(3x)−xe^(3x).   What are…

A:

Q: Obtain general solution. 1) y''-y=ex-4

A:

Q: The general solution of y' = X У can be written in the form = C

A:

Q: Find the general solution to (t² + 4)y' + 2ty = t²(t² + 4). Enter your answer as y = .... Use C to…

A:

Q: 4 y'+− y = 2; y(1) = −4 {y= X 2 = 5 -x-- 22 X 5

A:

Q: If ty'+y=6, y(1)=3 , what is the solution to the equation?

A: Consider the initial value problem: ty'+y=6, y(1)=3. Rewrite the equation:…

Q: 5. Given: f (x) = ax³ – 9x² + 2x – 4 and g(x) = bx³ – 5x² + 62x + 70 | Solve for all values of a and…

A: We have to find

Q: Find a particular solution to y"+3y'+2 y = x² - 3.

A: Given that,         y"+3y'+2y=x2-3  ⇒D2y+3Dy+2y=x2-3 Where, D=dydx ⇒D2+3D+2y=x2-3  Let, FD=D2+3D+2…

Q: 2.ryy' = y? - 2x. Find the solution that passes through the point (1,2).

A:

Q: xy" + xy² + 4y = /Nx Find the solution y(x)

A: We will find the solution of the differential equations.

Q: Q4- Solve y"- 4y' + 13y 3x.e*

A: Topic:- differential equations

Q: If u(x) = x3, then du = 3x2.

A:

Q: 1. If x²y-xy² + x² + y² = 0 find y'.

A: NOTE: As per our guidelines, I have solved the first problem. If u want the answer of other, kindly…

Q: If y= X 1-x +7x+9, find y' .

A:

Q: 20. '= 3 2 -1 2 1 -1, - (t) = -2t e² e³1 -4e¹-e-2t 2e3³t -e¹ -e-2t @3,

A:

Q: Use the method of Laplace transforms to solve the given initial value problem. Here, x' and y'…

A:

Q: (2) x (x+3)y"+2y'+y=0 solve for yox)

A: To solve the differential equation: x(x+3)y''+2y'+y=0 We can start by assuming a solution of the…

Q: The general solution to the ODE x²y" + 2xy' - 2y = 0 is y = C1x + C2x-2. Use variation of parameters…

A:

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.