In Problems 1–16 the indicated function y1(x) is a solution of the given differential equation. Use reduction of order or formula (5), as instructed, to find a second solution y2 (x). 8. 6y″ + y′ − y = 0; y1 = ex/3

Q: dQ 21. t + Q = t*Int dt 22. (2x + y + 1)y' = 1 23. (x2 + 4) dy = (2x – 8xy) dx | 24. (2r cos 0 sin0…

A: Divide both sides of the given equation by t to obtain standard form. tdQdt+Qt=t4lnttdQdt+1tQ=t3lnt…

Q: 19. (y² + 1) dx = y sec² x dy %3D

A:

Q: 3. Given the function y = (x² + 1)-1 + 3, suppose x decreases from 1 to 0.9. Find the absolute and…

A: We will find out the required solution.

Q: The indicated function y1(x) is a solution of the given differential equation. Use reduction of…

A:

Q: 4. Please answer all parts to the following diff eq. problem:

A:

Q: 1. Find the value of a and 3 so that the given differential equation is exact: (2y³ + axy¹ - 5x) dx…

A:

Q: 4.10. If y = f(x) = x – 6x, find (a) Ay, (b) dy, and (c) Ay – dy. (a) Ay = f(x + Ax) – f(x) = {(x +…

A: Given: y=fx=x3-6x

Q: 5. Solve the following differential equations using reduction of order. (a) y" - 4y + 4y = 0, where…

A:

Q: 14. y" + 4y + 4y = xe-x

A:

Q: For each dif erential equation in Problems 1–21, find the general solution by finding the…

A:

Q: In each of the following problems, use the method of reduction of order to find a sec- ond solution…

A: (c).The given differential equation is: t2y′′+3ty′+y=0;    t>0;   y1​(t)=t−1 Now rewrite the…

Q: 4. Find a second-order lincar equation for which y(x) = ce* + cze*z + sin(2r) is the general…

A: The homogenous part of the linear equation is, c1e3x+c2e5x. The particular part of the linear…

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.