10. Find u fram the differential equation and intial Condition. du u =e 2.9t-3.90 ul0)%33.2 dt

Q: write an equivalent first-order differential equation and initial condition for y.

A: An equivalent first-order differential equation and initial condition for y. y=ln x+∫xet2+(y(t))2 dt

Q: x² y' - 2lnx - e2y+4(Inx)/x = 0

A: Given: The given differential equation is x2y'-2lnx-e2y+4lnxx=0

Q: tate The Order Of The Differential Equation And Determine Whether It Is Linear.

A: Given that the differential equation i.e.       (i).   dydx=x2-y2.

Q: dr + t 4tx 0 dt dt3

A:

Q: Consider the differential equation.

A: Solution: The objective is to find r(t)

Q: Find U from the differential equation and initial condition. I'm know the answer but I don't know…

A: To solve below initial value problem.

Q: 2x dy 2х. -y = x² - x; y(4) =2 dx

A:

Q: y-3y+2y=2x +sin x+(1+2x)e" +4e* %3D

A:

Q: dy dy -4 =0 dx dx O 2 and 6 O 2 and 4 O 1 and 6 O 1 and 4

A:

Q: dy 1. tanxsin2y = sin²x + cos²y - dx

A:

Q: d²y dy e* - 2 + 2y = dx² dx cos(x)

A:

Q: 2) x – 1 = - 2e-y

A:

Q: Find the differential equation which has y= asinx+bcosx+xcosx

A: Given: y=asinx+bcosx+xcosx                                   ..1 for finding differential equation…

Q: Find the linear differential equation that is satisfied by y=xe-xsin3x+2e-xcos3x.

A: Let's find linear differential equation.

Q: d³u 2 dr5 d*u - 7- dr4 + 12 d³u dr3

A: The differential equation is given 2d5udr5-7d4udr4+12d3udr3+8d2udr2=0. Here ,s=ddr then equation…

Q: 2. [e2y ycos (xy)| dx + 2xe2y [2we?y xcos (xy) + 2y dy = 0 -

A: The solution is given as

Q: From the differential equation dy = x2 dx, what is the equation of y in terms of x as the curve…

A: Given: dy=x2dx

Q: 4. t dv + (v – v² ln t)dt = 0

A:

Q: 19. (5x2 — у) dx + xdy %3D 0

A: Given (5x2 -y)dx + xdy = 0 (5x2 -y) + xdydx = 0 Calculate whether the differential equation is exact…

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.