You should be able to solve a differential equation that is/can be solved by: ⚫ separable ⚫ linear ⚫ exact ⚫ a substitution (homogenous, Bernoulli's or Ax + By + c) Practice Problems Solve the following differential equations 1.(y²+1)dx = y sec² xdy dy 2. x(x+1)+xy = 1; y(e) = 1 dx 3. dy - y = e² y² 4. (x + y³)dx + 3xy² dy = 0 dy 5. + 2y = 1; y(0) = dt 6.(y²+yx)dx+x² dy = 0 - dy 2xy) = dx =y(y+ sin x); y(0) = 1 7. ( + cos x 1+y2 1-x-y 8. = dx x+4 dy dx 9. (x² - 1) + 2y = (x + 1)²

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Using the Method of Undetermined Coefficients, determine the form of a particular solution for the differential equation. (Do not evaluate coefficients.) 3 y" + 64y = 9t³ sin 8t The root(s) of the auxiliary equation associated with the given differential equation is/are (Use a comma to separate answers as needed.) Write the form of a particular solution. Choose the correct answer below. OA. Yp(t)=t(A3t³ + A₂t² + A₁t+ A₁) e¹ cos 8t + t ¹ cos 8t+t(B3t³ + B₂t² + B₁t+Bo) e' sin 8t O B. Yp(t) = (A3t¹ + A₂t³ +A₁t² + A₁t) e' cos 8t + (B3tª + B₂t³ + B₁t² + Bo) e' sin 8t OC. Yp(t)=t[(A3t³ +A₂t² +A₁t+A₁) cos &t+t(B3t³ + B₂t² + B₁t+ B₁) sin 8t OD. Yp(t) = (A3t³ + A₂t² +A₁t+A₁) cos &t+ (B3t³ + B₂t² + B₁t+Bo) sin 8t

Need help, round answers to 3 sig figs please

Please write the answer in a paper and apload it because I cannot see it if you don't wrote it in a paper thank you

Q2

Write a MatLab code to solve these 4 equations

Points for stress vs strain (in image) Assume the compressive concrete strength (f’c) is 3,000 lb/in2 (psi)Calculate a cubic function (3rd order polynomial – Ax3+Bx2+Cx+Constant)Use this function to create a function that describes the slope of the cubic function (the derivative of thecubic function). This new function allows you to calculate the tangent to any point along the curve. Thetangent is the modulus of elasticity (E).   The concrete code provides a formula to calculate E for concrete. That formula is:E = 57,000√??′, where f’c is in units of psi, and E is in units of psi.Use the derivative function you calculated to locate the point on the curve where the slope of the curvematches E using the concrete code formula. Express that stress point on the curve as a percentage ofthe compressive strength of the concrete. Now, calculate the secant modulus for the test case using 1,500 psi (50% f’c) as the arbitrary point onthe curve.Assume fracture occurs at the last point…

Please handwrite and solve part a and b, thanks.

solve erf one