Solve the initial value problem dy y = 5e" + 28e5* dx with y(0) = 8.

Q: Solve y" + 3y" – 3y' – y = x+ e².

A:

Q: 5) Solve the Non-linear second ODE: d²y 3 x² y- 2 dy + y? = x2 \dx) dx2

A: Given: 3 x2yd2ydx2+y2=x2dydx2

Q: Suppose that x and y represent the amounts of two basic inputs for a production process and…

A: Suppose that x and y represent the amounts of two basic inputs for a production process   The…

Q: Identify the first order DE and show the solution for (x-x^3ye^-2y)dy-dx=0

A: Given the differential equation

Q: Solve y" +5y' = (2x+1)e" -5x

A:

Q: 6) Solve for y: 3"*1 = 9"-1

A:

Q: Solve (D² – 3D + 2) y = 2e3 +4 sec (e-)

A:

Q: Let y = Arcsec (cos² 3x). If y '= == A (B C) D) - 6 tan3x - 3 sin3x - 6 sin3x cos3x N 2 cos3x D and…

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: D. Exponential shipting Theorem (D°+ 10* - 30 - 18) y = 24 x ° e-s* -3x 4.

A:

Q: dy 3y Vx +1+x = 0, y(0) =1 dx

A: Explained below

Q: 4. Solve dx -dy = 0 %3D x²y xy?

A:

Q: Find d2y/dx2 if e^y− y = x. Write your final answer in terms of x and/or y, and simplify.

A:

Q: Solve 4 x*dy +y*dx = 0

A: The given differential equation is: x4dy+y4dx=0x4dy=-y4dxdyy4=-dxx4

Q: Solve 16y" – 8y" + y' = 0

A: Write the auxiliary equation first and find it's roots.

Q: Solve (1+x)dy-ydx=0

A:

Q: Solve y'' − 4y' + 4y = 3e2t

A: Solve y'' − 4y' + 4y = 3e2t

Q: solve by bernoulli y' + (8/x)y = x6y4

A: We will find out the required general solution for given Bernoulli's equation.

Q: х3—125 dy 5. у %3 х2+5х+25' dx х-1 + x+1 dy 6. у %3 б. dx

A:

Q: Solve dx+ dy 0

A:

Q: dx² dx 543-5+ y = 0; y(0) = 4y'(0) = 0

A: To solv the following initial value problem.

Q: Solve the bernoulli equation dx/dy+(2/x)y=-x^2y^2cos(x)

A:

Q: TV Cos X 4-3 Sin x dx 2. Calculate

A: Solution

Q: 2.Solve bernoulli (x ^ 2 + y ^ 2) * dx - xydy = 0

A:

Q: 5- (2xe" + e')dx + (x² + 1)e³dy = 0

A: solving given DE by separation of variables.

Q: Solve for y. y' = 7x + xy​; y = - 4 when x = 0

A: Given,  y'=7x+xy,  y=-4 when x=0

Q: Solve ry + (2r* – 1)y = 4x*e %3D

A: Solving the first order differential equation

Q: 10/ (3e"y-2x)dx + e"dy = 0

A: We have to find the general solution of differential equation

Q: f y=y(x) is the desired solution of 2 = f(x,y), Derive Euler %3D teration formula for solving ODES…

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.