3. Choose one of the following first-order equations to solve. dy (x² + 1): + 3x(y – 1) = 0 dx а. %D

Q: d²y when x = 1 for the equation x²y – 4x = 5. It is known that dy 4-2ху Find the value of dx2 dx x2…

A: Given that the equation: x2y-4x=5 Differentiate the given function with respect to “x” then,…

Q: Solve: (dy/dx) = [(5y – 2x) /(4x - y )] %3D

A:

Q: 3. fip dx = x+y+1

A: According to our guidelines we are supposed to answer only one asked question.kindly repost other…

Q: 2x If y= e, then %3D dx² a. 2x O b. 6e²x 2x 4e²* Od. 2e²*

A:

Q: Solve dy = y, y(0) = 1byPicard'smethod and comparethesolution with theexact solution.

A:

Q: Approximate y(0,2); = 3x + y; y(0) = -1; Step size: h = 0.04 dx %3D %3D

A: Given: The differential equation is dydx=3x+y;y(0)=-1 i.e., x0=0, y0=-1Step size , h=0.04 Euler's…

Q: w=z/3y−x, solve for y.

A: The given equation is

Q: d²y from the following dx2 Solve 1. y = 8x* – 12 x° + 6x² – 9 2. y= (4x-9)?

A:

Q: %3D =D3e %3D 4.

A:

Q: 1. Separating the variables dy 1 x(y- 3) =D4y dx %3D

A: In the separation of variables method of solving the differential equation, the different variables…

Q: Solve for the value of C in the equation: dx 3y³ II (1-2x)dx 3 when y(0) = 1

A: The given differential equation dyy4+dx3y3=1-2x3dx We have to find the value C when y0=1

Q: Find

A: We will find the derivatives.

Q: = -secu a

A: Given : y=f(u)=-secu and u =g(x)=x2+7xwe have to find d2ydx2

Q: 5. Solve: 4xy2(3x³y – 5xy) = 0, Let y = 2 %3D

A: A detailed solution is given below

Q: - 2y 4 given that y = 3 and 4 when x = 0. Solve dx2 %3D %3D dx

A:

Q: D.E Poll owing (1+y)dx= (bany -x) dy Solve the %3D

A:

Q: 1. xy' – y – 5x* – 3x² + 2x = 0 when x = 1 and y = 2 н. ху' —

A:

Q: dy Q1: - Find of the following functions dx y = (x +) (x –+ 1 a. %3D - x2+3 b. y = %3D (x-1)3+(x+1)3

A:

Q: Stue; dy = (1-x)y²+ (2x-Dy-x given Sdutfon y-1 %3D

A:

Q: 3. Find dy of the following equations: dx a. y = |(e-3x² + 7x² + In 8x

A:

Q: Solve the DE 3y2 Y +x-1y3 =x*. dx

A:

Q: 5. Give an equation, for y = v4 – x2 compressed vertically by a factor of 3 %3D

A: We know that when the graph of f(x) is compressed vertically by a factor'C'.  Then the transformed…

Q: Solve for the value of C in the equation: dy − (y + xy5)dx = 0 when y(0) = 1

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.