Solve the given initial-value problem. The DE is homogeneous. ((x^2)+(y^2))dx/dy=xy,  y(-1)=2

Q: (3y? + 2)2 = 1 and y(-1) = 1 What is x when y = 2? %3D dx

A: solve the differential equation by separating the variable and integrate it.

Q: 2y′ + y = 3t2

A:

Q: Solve: (xy – 1) dx + (x² - xy) dy = 0 %D |

A:

Q: Solve (yz + хуz) dx + (zx + хуz) dy + (ху + хуz) dz =

A:

Q: Separate the equation (1 + x + y + xy)y' =x.

A: First, convert the expression on the left-hand side in product form and then separate the equation…

Q: Determine an expression for expression for 3(y-2)³ − x² = 4x − 6. dx

A: Solving the problem by finding the value of the problem by finding the value of the derivative.

Q: B. Solve DES: (x+y) dx + (3x+3y-4) dy =0 C. Solve DES: y' + y = x/y

A: Given: It is given that the equations are x+ydx+3x+3y-4dy=0 and y'+y=xy. To find: The main objective…

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.