dt = ry + D v

Q: tant dt 9,

A: To find the given integral ,use the substitution u=tan t .

Q: dy 4. Let ry = 2 and dt dx when x = 1. dt Find

A:

Q: sech Vt tanh V dt Vi

A: Given : Intergral sech √t tanh √t dt / √t

Q: Solve simultaneous equation dx/dt=x+y , dy/dt=4x+y , t=0 , x=2 , y=5

A: First I have written the differential equation into operator form and then reduce it into linear…

Q: [(x²-y²)²] x+y -2 LEK 1J0 du dt

A: We have to find value of given double Integral.

Q: dt || y whent = 0, y =

A: Please refer to the image below

Q: dx 2х — dt dy – y = 6e3t, dt. dx 2 dt dy 3x + dt - 3y = 6e3t; %3D x(0) = 3, У (0) — 0. %3D

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Integrate by Substitution. 1. dx where u = Vx+2 2Vx+2

A: By using substitution method, we calculate the given integral.

Q: dy dt t2

A:

Q: dx + 3tx = t4 Int+1, dt 2. t2. %3D

A:

Q: dt dy 글 + 1y dt

A:

Q: vt e dt

A:

Q: Find dt y = 6t + /9+ 7-t dy dt |3|

A:

Q: = Lasin(t") dt y%3D

A:

Q: EXERCISE 1 dy -dx = 0

A:

Q: Convert the differential equatim Inte c System and Solue the sustem: T0-20+3),=D0

A: See the attachment

Q: If y = x + ex, find dx/dt.

A: Given query is to find the derivative of the expression.

Q: find the integrating factor (x+1)dy - (2y+2x+1)dx = 0

A:

Q: :Use variation of parameters to solve dx Зх — Зу + 4 dt dy 3D 2х — 2у — 1 dt

A:

Q: dz %3D dt

A: Given that: z3=x3+y2, dxdt=2, dydt=1 and z>0.

Q: S sin Vat dt

A: Let the given integral be: I=∫sinat dt

Q: 2 In sec Vi + tag V + C sec sec z dz %D

A: 35. given integral,∫sec x . dxx = 2∫sec x12 . 12x-12dxlet x12 = u⇒ 12x12-1 dx = du⇒12x-12dx = du

Q: Find dy/dt.

A: Find dydt.

Q: d csinx 1 dt 1-t2 dx '3 V5 SNt VE2 + 1 dt 1+xv

A: We have to solve the integral

Q: A. = 2x - y + sin2t dt = 4x + 2y + 2cos2t (variation parameter). dt

A:

Q: Find the Integrating Factor of dy + 2ytanx = sinx dx

A: This is 1st Order Linear Differential Equation.

Q: y'' + 3y' + 2y = sin ex

A:

Q: Vēt VE dt

A: Our Aim is to evaluate the integral given below:-

Q: TO Show Jv - x-V そーレ V+ dx

A: Jvx = ∑m=0∞ -1mx22m+vm! m+v!

Q: Find the integrating factor of (x^2−y^2−4y−5)dx+2x(x+y+2)dy=0

A:

Q: Find dy/dx

A:

Q: Find dv if v = t- dt |

A:

Q: Find dy/dt when x=4 and dx/dt=-3, given that x^3+y^3=72

A:

Q: dt 1 . sec t

A: Given integral is ∫dt1−sect The expression 11−sect can be written as follows 11−sect=sect1−sect+1…

Q: Integrate both sides dy = -dx

A: the given integral equation is                             ∫1y2dy=∫1xdx

Q: dz + et+z = 0 dt

A:

Q: dz/dt = -Bz(1 – vz), z(0) = 1. %3D

A:

Q: calculate the derivative.

A:

Q: sinx2 dy Find dt

A:

Q: dz dt 3x – 2y fip dt 9x - 3y %3D z(0) = 1 %3D

A:

Q: sech 2t dt Evaluate 3, coth 2t

A:

Q: 9. dx/dt = −(x − y)(6 — x − y), dy/dt=x(4+y)

A: Given that, dxdt=-x-y6-x-ydydt=x4+y We have to determine all critical points of the system of…

Q: ds Find where Vt +s = 2s . %3D dt

A:

Q: Find dt y = 31(21? – 5) $ dy dt

A:

Q: dy/dt=0.3(y-200)

A: Separate the variables and integrate both sides.

Q: t sin (=) dt du

A:

Q: zp dt

A: we have to solve the differential equation. dzdt+2et+z=0

Q: dy dt II

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.