Classify each differential equation as an ordinary differential equation (ODE) or a partial differential equation (PDE), give the order, and indicate the independent and dependent variables. If the equation is an ODE, indicate whether the equation is linear or nonlinear. d.x et = 4t – 2 dt ODE or PDE: Order: Independent variable(s): Dependent variable: Linear or nonlinear: ди 2 du (b) dy ODE or PDE: Order: Independent variable(s): Dependent variable: Linear or nonlinear: 1 dy a dr3 (c) - sin(x)y = x?y ODE or PDE: Order: Independent variable(s): Dependent variable: Linear or nonlinear:

Q: Se csc x dx

A: Given: I=∫cosecxdx For evaluating given integral, we multiply and divide given expression with…

Q: x -Jx-15 = 3 Salvethe equation

A: We have to solve the equation                                              x-x-15=3

Q: 1X-31 dx -2

A:

Q: A cup of hot coffee initially at 95°C cools to 80°C in 6 min while sitting in a room of temperature…

A:

Q: 1 3 dr Ip %3D

A: In this question we have to find Integration.∫ax=axln+C Formula Used,

Q: S cor 3ydx có

A: We need to find integral value.

Q: S 2³x dx = 0 23x+1 3x+1 23x In 2 O O O + C + C 23x + C In 8 2³x In 2 + C

A:

Q: 1- 3t - 2 t+1 - dt

A:

Q: Pr[A U B] = 0.90, Pr[A] = 0.70 and Pr[B|A] = 0.40. Find Pr[B].

A: Given data, P(A U B)=0.90 P(A)=0.70 P(B|A)=0.40 P(B)=?

Q: d Calculate dt

A: To calculate  ddtt2et

Q: jn= 16, α=0.05

A:

Q: dy +Zy =0 du

A: Given: dydx+2y=0   We know that; ∫1ax+bdx=1alnax+b+C And ∫a·fxdx=a·∫fxdx, where 'a' is the constant.…

Q: -2x +5 Evaluate 10-4x -2y dy dx 3x 25 3

A: The given integral is: ∫01∫3x-2x+5(10-4x-2y)dy dx

Q: dx 2. S sec4xcot4х

A:

Q: Find dx

A: Please see the answer in Step 2

Q: erty' (t) = -8

A:

Q: dx 1-

A:

Q: - 4× dx хе

A:

Q: The windchill index announced during the winter by the weather bureau measures how cold it "feels"…

A:

Q: Next, simplify. - 3t dt = dx

A:

Q: dz

A:

Q: Xe dx

A: The detailed solution is as follows below:

Q: ZB = %3D ZA = %3D AB=

A:

Q: 4 xp£

A: We have to find the integral.

Q: Find the positive solution of f = 2x – cosx

A:

Q: SVī dx

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.