5) Verify that y = 2e3 – 2x – 2 is a solution to the differential equation y' – 3y = 6x + 4. - -

Q: 1. y = c1e-2x + cze²x + cze2x 2. y = c1e* + cze3x

A:

Q: Obtain the differential equation whose general solution is y = ₁ + ₂³x A. B. |y" - 3y' = 0 D. E. 3y"…

A: Differentiate both side with respect to x

Q: (2x + 3y – 5)dx + (3x - y - 2)dy = 0 Solution:

A: Given the differential equation(2x+3y−5)dx+(3x−y−2)dy=0

Q: Solve the ordinary differential equation 3xy" + (2 - x)y - 2y = 0. Then evaluate the first four…

A:

Q: (D – 3D + 2) y = (1+ e-")?

A: I am attaching image so that you understand each and every step.

Q: The solution to the differential equation (x²2 -4xy-2y²)dx+(y² -4xy-2x²)dy=0 a. y²(y-6x)+x²(x-6y)=c…

A: To find the solution of the following differential equation. x2-4xy-2y2 dx+y2-4xy-2x2 dy=0

Q: Form the Differential equation if its solution is V=acos(2x +b) O a. y'= 2x b. None of these O c.…

A:

Q: a) Find the first three terms of two linearly independent solutions for the given differential…

A: Given- 9x2y''+x2y'+2y=0 To find- The first three terms of the solution of the above differenial…

Q: 2. (2x– 3y +1)dx - (3x + 2y – 4)dy = 0 |

A:

Q: 3. a) Use the substitution u = -x+3y to solve the differential equation. -x+3y)y'= 1 b) Clearly…

A: After substitutions, separate du and dx.

Q: Obtain the differential equation by eliminating all arbitrary constants. 1.) y² = Ax² + B secx

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.