For the differential equations below, write in standard form, and name the type of equation. Then give and make the appropriate substitution so that the equation is in terms of the new variable and is in standard separable or linear form. You can stop.once you get to standard separable or linear form. You do NOT have to find the general solution. a) x'y'+2xy =5y

Q: 2 Solve for y. 3y-9 y = y+12

A:

Q: Find a general solution. y₁ = y₁ + 2y2 + e²t Y2 = -32 +42e-2t NOTE: Write arbitrary constants as c₁,…

A: Linear differential equation  where  are functions of x or constants.Then Integrating factor (I.F.)=…

Q: B Electrical condenser An electrical condenser with initial charge Q, is allowed to discharge.…

A: Given equation is: Q=Q0ekt We have to solve this equation for t.

Q: x2+y2=z2  for y>0 Solve for y. Express your answer in simplest and exact form.

A: We have given equation  x2+y2=z2 for y>0 y2=z2-x2 y=z2-x2 As y>0 y=z2-x2

Q: Rearrange the equation to solve for x. a = h(c+x)

A: a = h(c+x)

Q: Solve for y. Give an exact answer. 2y - 5 = eln(20) y =

A:

Q: Solve the rational equation: 8. 3. 3x + 22 | X - 2 x + 1 х - х-2

A: The objective is to solve the rational equation.

Q: Write the non-arbitrary parameters in terms of the arbitrary ones. x+1y+1z=-8 −3x-2y+1z=15…

A: Solution:

Q: y" – y = 2xe". Y' %3D

A:

Q: solve for y. y is a real number. 1=(the square root of 3y+6)-1

A: when we solve an equation, perform same operation on both sides of the equation.

Q: Solve ++ 2t with respect t. 2x+t e = e

A:

Q: Solve the following equation using the zero product law. 2x² –13x – 24 = 0

A: Solve by factorisation method.

Q: x2 - 4ху- 2у2-2 %3D0 4xy to

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.