5. Show that the equation (2y – 6æ) dx + (3x – 4x²y=') dy = 0 is not exact. Show that the polynomial µ(x, y) = xy² makes the equation exact. 6. Solve the equation in 5.

Q: 7. Find d²y dx² from y = √√x- =√x-²/2

A:

Q: . Find the general solution of the first-order equation y? – 2ry dy dr

A:

Q: 1. (x + √y² + 1) dx · (y – H.W. solve the following D.E. xy - - √12241) dy = 0

A: Step 1:

Q: Solve by reduction of order. Find y2 and y (x² + 1)y" – 2xy' + 2y = 0 yı = x -

A:

Q: Suppose that Yı x5 is a solution to x²y" – 10xy' + 30y 0. Use reduction of order to find another…

A:

Q: Q5. Use the method of undetermined coefficients to solve (a) y" +2y' + y = x²e¬ª. (b) у" — 2у/ + 5у…

A: We are entitled to solve only one question at a time. As the specified one is not mentioned, So we…

Q: 8. Solve the Cauchy-Euler equation 4x²y" + 8xy' + y = 0.

A:

Q: Select all equations that are equivalent to a-6z 16. a + 6x 9 0 O b a + 6x +9 = 16 Oc a+6x + 9 = 25…

A: Solution:-Given equation,     x2+6x=16  —1let us see and solve each option given,a…

Q: ¸¸ S'√ 16–16 x² d x = · (a) 16 π (b) π square unit. ©2π (d) 4π

A:

Q: 1 14) Find xe™³x² dx . | 0

A:

Q: 2y" - 5y' + 3y = 14te²¹

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.