2. Solve the initial value problem and the boundary value problem d²y | 2 – 16 + 50y = –14e¬t + 10t³e=t | y(0) = 0, y'(0) = 1, 2 – 164 + 50y = –14e-t + 10t³e=t |y(0) = 0, y(1) = 1. %3D (2) (a) Find the general solution of corresponding homogeneous equation.

Q: (2x+1) (x+1) y"+2xy' - 2y = (2x+1)- A solution of the homogereous Jorm is → y= (x+1)-1 Find the…

A: The differential equation is provided below, 2x+1x+1y''+2xy'-2y=2x+12 And one of its solution is…

Q: 10. Find the general solution of (2y) dx + (x - x'y) dy = 0. A. x*y - 2 = Cx?y B. x'y + 2 = Cx?y C.…

A: Let's find.

Q: x²y" − x(x + 2)y' + (x + 2)y = 0, 0 < x

A:

Q: 5. Find a second solution to (1 – a2) y" + 2xy' = 0, given one solution y1(x) = 1.

A:

Q: 1) Find the Solution. a) (y" - 5 y² + 4y = 0 y(0)=4 5) 4'(0) = 0 " 4" "y" + "y' 4(1) = 5 y' (1)=10 +…

A: We have to find the solution of the given differential equation.Note: According to the guidelines we…

Q: c. y' + 2y = x³ with y(1) = 2 Yo (x) = e Yp (x) = y (x) = y (x) = -2x 1½ e ²x³ - 2/ ( 10²x² -…

A:

Q: (8) y'= 4x +x? -y, with y(0) = 4, h = 0.05, find to 3-decimal.

A:

Q: Find a continous solution satisfying the equation and the initial condition (1+x²)y/ +2.ry = P(x) r,…

A: we have given a first order differential equation with piecewise function P(x) we need to find a…

Q: A second order Caushy - Euler equation having a solution y(x) = x²cos(4Inx) is %3D x²y" + 5xy + 16y…

A:

Q: 2c) find the general solution to 9y"(x) +12y'(x) + 32y(x) = x +e*

A:

Q: 4. Use undetermined coefficients to find a particular solution to x=2x+3y+5, y' = 2x + y = 2t.

A: Approach to solving the question:To find a particular solution to the system of differential…

Q: 1. If y = In(V x² +1 ) , then y' = 2x (b): 2x (a) x² +1 3(x2 +1) () 3(x2 +1)-2/3 (d) 3(x2 +1)

A: y=lnx2+13⇒y=lnx2+113⇒y=13·lnx2+1   ∵lnxy=ylnx

Q: 2. Solve IVP y" – 4y' + 4y = 0; y(1) = 1, y'(1) = 1 Cind a general solution

A:

Q: 3. Find the correct form of x(s) and stop. State x(s) as a single fraction. x" +7x' + 6x = 2t x(0) =…

A: Explanation of the answer is as follows

Q: Question 1 Consider the following IVP: y"-2y'= -4; y(0) = 0, y'(0) = 4 Find the general solution. A…

A:

Q: 3. Find the solution of the DE 2yy" = 1 + (y')², x > 0, y > 0.

A:

Q: 3) Given that y₁ = ex is a solution to the ODE xy" + 2(1-x)y' + (x-2)y= 2e* Find a solution for y2

A:

Q: 12. G dr/de = p2/0, r(1) = 2 %3D Answer -1/2 Gy = ry (1+a)2, y(0) = 1 13. %3D Answer 14. Gy = 2x/(1+…

A:

Q: The differential equation –y" = f(t), y(2) = 0. y(5) = 0 discretized with step-size h = has the…

A:

Q: 1) Find the Solution. a) (y" - 5y' - 4y = 0 4(0)=4 4'(0)=0 b) Y" + '4y' y(1) = 5 y' (1)=10 + My = 0…

A: For the given differential equation,The aim is to find the solution of the differential equation

Q: Determine the value of k such that y=4x²-3e²t is a solution to x(1-x)y"+ (2x²-1) y'+k(2x-1)y=0

A:

Q: Find the solution of the differential formula in partial derivatives = x³ sent +1; y(x,t);…

A: Integrate twice with respect to t and then put conditions

Q: What is the particular solution of y'=x²-2x+3, ify=4whenx=0?

A: What is Ordinary DIfferential Equation: A differential equation having one or more functions of one…

Q: 2. Find the general solution of xv + 1) dx + y(x - 1) dy = 0 2x - 2y + %3D x2 - y2 + 2x - 2y +…

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

Q: 3. (1−x³) d²y dx² DE -+ (sin x)y' − 3xy = ln x(+1) TYPE ORDER DEGREE LINEARITY

A: Need to write down the type, order, degree and linearity of the given differential equation.

Q: (10) Solve the given BVP by using Green's function: ; (ii) y" – y/ = e2; y(0) = 0, y(1) = 0

A: Given differential equation is: y''-y'=e2x y(0)=0y(1)=0 Green function in equation is given by:…

Q: Find the general solution of the following DE. y' = 3 (y + 1) O y = 3ce³x - 1 Oy = ce³x - 1 Oy =…

A: y' = 3(y+1) dy/dx = 3(y+1) dy/3(y+1) = dx dy/(y+1) = 3dx now apply both side integration

Q: Find L(y). / + 2x = 2 - x' = et (0) = x (0) = 0 -2 L (y) PL(y) = %3D s(s2 +2) 2s L (y) = %3D…

A:

Q: 4. Find the complete solution of 2x³y' = y(y² + 3x²) %3D

A:

Q: Consider the following IVP: x" - 4x' + 4x = 4e2t; x(0) = -1, x'(0) = -4 Find the general solution. A…

A:

Q: The solution of the differential equation (xy – y²)dx – (x² + y²)dy = 0 is : %3D A) 2 In + 1| – In |…

A:

Q: 5. The exact equation (3x2y+e")dx + (x³ + xey-2y)dy = 0 has the general solution 2² - 2xy (A)…

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.