16) Solve the differential equation (ædz + ydy + zdz)²z = (2 – 2² – y3)(zdx + ydy + zdz)dz

Q: dy + (3х — 7)у 3 5x7 | dx

A: Consider the provided D.E,

Q: Find all solutions of y" = ln x

A: We have to the differential equation.

Q: (2xy + 3y²) dx – (2xy + x²) dy = 0 .. [VARIABLE SEPARABLE/HOMOGENEOUS |

A:

Q: 5. Solve (y² + 3xy³) dx + (1 - xy)dy = 0.

A:

Q: B. ty" – (t+ 1)y' + y = t?

A: Answer is mentioned below

Q: (6xy + y² − ysin(xy))+(3x² + 2xy-xsin(xy))dy = 0

A:

Q: 4. Solve the following DE: (2x²y)y' = x³ + 2y³

A: Given in the question, The diffrential equation is as follows:- By dividing both sides by 2x2 * y3,…

Q: Solve by undetermined coefficients. y" – 3y' = 6e – 2e", y(0) = 0, y (0) = 0.

A:

Q: 4. Using homogenous D.E approach, solve (x³ – 3xy?)dx = (y3 – 3x²y)dy.

A:

Q: 2ty t²+1 – 2t – (2 – In(t² + 1))y'

A:

Q: Solve the differential equation ydx (2x + 1) (da – dy).

A:

Q: 5 dy dx √√x²-4x 9. Find the general solution to the differential equation: *Solve for y. Indicate…

A:

Q: (b) Use the substitution u = x In y to solve the equation (xy + 2ry ln² y + yIn y)dr + (2x² In y…

A:

Q: I241 Solve the DE. (3x²y- xy)dx+(2r'y² +x*y*)dy = 0.

A:

Q: (b) Solve the IVP (3xy – y²)dx = (xy – x²)dy y(-2) = 3 - %3D %3D

A:

Q: Solve for the value of constant C in the equation: (2x + 3)y' = y + (2x + 3)¹/² when x = -1 and y =…

A:

Q: - 4. 3y(x² − 1)dx + (x³ + 8y − 3x)dy = 0; when x = 0, y = 1

A:

Q: Solve for the value of constant C in the equation: (2x + 3)y' = y + (2x + 3)¹/² when x = -1 and y =…

A: Given:- 2x+3y'=y+2x+31/2

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.