Given the initial value problem [4 (t) 2 (t) –10y1 (t) – 11y2 (t) + 50 cos(5t)]' Use Forward Euler's method to approximate y (t) at t=20 using h=0.05. Round your answer to the nearest ten-thousandths.

Q: [4xe y + 3 sin (2x) ]dy + [2e-y + 2 cos (2x) ]dx = 0

A:

Q: 18. Verify that the result (f(t)} = sI (f(t)} - f (0) for (a) f(t) = t2 + 2t – 4 and (b) f(t) = cos…

A: Note: According to Company Guidelines we are providing the answer of first question. Kindly post…

Q: Suppose the cost per hour incurred in operating a cruise ship is 5a + b^4v^3 dollars per hour, where…

A: Step:-1 Note:-  your cost expression is not clear here as it can be 5a+b4v3   or   5a+b4v3 , So i am…

Q: Find i (t), given 7(t) = (5 cos(– 2t + 3), 4te', – 2t In( – t)). %3D F (t) =

A: To find the derivative of the given parametric vector, we need to differentiate each component of…

Q: Q.4 (a) Use the formula S.{f"(z)} = af(0) – a*S.{f(x}} to find Sa{cosh(2r)}. (b) Classify the…

A: Given In part4a:Sαf''x=αf0-α2SαfxIn part4b: yuyy-xuyz+uy=0

Q: On a piece of graph paper, create an amplitude vs. time graph of a sine wave with an amplitude of 5…

A: Formula: Frequency=1Period. Given: Amplitude = 5 Pa Period(T) = 0.03 sec. To find: Frequency(f).

Q: olve the following initial value problem using variation of parameters: y" + 4y = cos 3x y(0) = 0,…

A:

Q: What is the Smoluchowski equation for the harmonic: V(x) = (kx2)/2

A: The Smoluchowski equation is a partial differential equation that describes the time evolution of…

Q: 6. d dx sin x f 1 t√√t² dt +2

A:

Q: Find the fourth iteration value of an extremum (maximum/minimum) value of the image if a = 4, b =…

A: For the given values of a, b and c, we get, f(x)=4cos1.5x+2x-3

Q: dy 50(1 + cosx) – 0.05y, 0<x< 2π dx (0) 200

A: Given an ordinary differential equation with initial values.

Q: Find the general solution to x′′(t) + 4x(t) = tan(2t) using variation of parameters. (Notice that…

A:

Q: 5.. Find the general solution to the DE using the method of Undetermined Coefficients: y" – 4y = te'…

A:

Q: 6. If P (t) = 2 sin t, then find P(19) 2πt 3

A: given P(t)=2sintwe know  d dt(sint)=costd dt(cost)=-sint

Q: (cos t)y" + (sin t)y' – ty = 0,

A:

Q: - ual2) V17 – cos(27at) (2 – 4t) sin(#) Given f(r) = edt, find the equation of the line tangent to…

A:

Q: 2xyzx − xzy - 2yz = 2x²y cos(x + y²)

A:

Q: Q2- Solve the following P.D.E (1 - sin x )U, – Ux = 0 , using the condition , U(0,0) = 4 and U(0,1)…

A: we are solving this using integration. here Uy=dU/dy and Ux=dU/dx

Q: 2. A particle moves along the x-axis so that at any time t > 0, its acceldration is a(t) t = 0, the…

A: Given,           at=32cos2t

Q: Given the functional equation $(1 – s) = (27)-ª.2. cos ()r(s)<(s). Show that {(s) = {(1 – s), where…

A:

Q: Find L(f(T)), given a. L[(sinT)µ (T – 3 b. L[(cos (T – )µ (T –: 3n. 2 2

A: We have to find Laplace transform of given function.

Q: By making a suitable change of variable, solve the ODE dy dx Rewrite the solution as an explicit…

A: In this question we will find the solution of the differential equations.

Q: Find F(s). L{(1 – e° + 4e-6t)cos(2t)} F(s) =

A: Here we have to find laplace transform of given f(t) .

Q: Find the general solution of the following exact differertial equation (e Ax + 2xy²)dx + (cos y +…

A: Givne that  The following differential equation  (e^4x+2xy^2)dx+(cosy+2x^2y)dy=0  To find the…

Q: Question 5 Solve the following initial value problems. dy (a) = 6 – 2 cos(3x) and y(0) = 10. d.x dy…

A:

Q: Find T(t) and N(t) at the given point. r(t) = 5 cos(t)i + 5 sin(t)j + tk; t = 2 T(₁/) = N (₁) =

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.