19. Solve the following differential equa- tions using classical methods. Assume zero initial conditions. [Review] dx a. +7x = 5 cos 2t dt d²x dx b. d1² + 6 + 8x = 5 sin 3t dt d²x dx C. dt² +8+ 25x = 10u(t) dt

Q: Option 2: Problem Solving You wish to invest P10,000 for a period of 5 years. Which of the following…

A: The principal amount we have is ₱10000 and the time period is 5 years.  Therefore,  P=₱10000 t=5

Q: 1. Find the differential dy in y= 2x4-3x3-5x 2. Use differentials to find approximate values for…

A:

Q: 1) Solve the IVP: y" + 2y' + 2y = 5 sin t + 5 cos t : y(0) = 1 and y'(0) = 2

A: Given initial value problem is  y''+2y'+2y=5sint+5cost, y(0)=1, y'(0)=2. Let y'=dydt=Dy and…

Q: Find a linear operating point model of the differential equation: d²x dx + 3 + 2x = sin x dt2 dt a)…

A: Consider the provided question, Given D.E, d2xdt2+3dxdt+2x=sinx We need to find a linear operating…

Q: dy a) = cotx cot y dx b) (x² + 1) dy dx = xy² + xy = c) (1 + x)2 dy dx + y² = 1

A: Let us consider a differential equation of the form dydx=f(y)g(x) Then the differential equation is…

Q: 2. Find all solutions: dt dy dx = 4x + y x + 4y' x > 0.

A:

Q: Q1) Solve the following partial differential equation Ux + Uy = (cos x + sin y). U

A: 0

Q: 2. Use the substitution technique to find [*5'sin(5¹) dt exactly (not an approximation).

A: The given integral is ∫015tsin5tdt use the formulas, ddtat=atln(a)∫sint dt=-cost+C

Q: 5. ex+ydx = dy χ

A: “Since you have posted multiple questions, we will provide the solution only to the first question…