Transform the given differential equation into an equivalent system of first-order differential equations. ²x" - 6x² + (1 -t²) x = 0 Let x₁ = x and x₂ = x'. Complete the system below. x₁' = 7 x₂ = 0

Q: Determine whether y = 2x is a solution of the differential equation y'= 6x², a. 6x2- and by'= 6r?…

A: Just take derivative of y and substitute in given differential equation and see if it satisfies the…

Q: 3 X' -3 5

A: This question related to system of ode.

Q: (x2 + 1)у' + 3x(у — 1) — 0, У (0) — 2

A:

Q: 2. 2xy dx + (x2 + y2) dy = 0.

A: Given diffrential equation 2xydx+x2+y2dy = 0 dxdy=-x2+y22xy....(1)

Q: Form the differential equation of family of lines situated at a constant distance p from the origin.

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Solve the differential equation using Separable of variables.

A:

Q: (1– x){ - 4xÍ +5y = COSX dy. %3D dx2 lx

A:

Q: Find the differential equation by eliminating the arbitrary constants of the family of curves y = C₁…

A:

Q: Use variation of parameters to solve the differential equation x²y" + 10xy' + 8y = x².

A: The given problem is to solve the given differential equation by using the method of variation of…

Q: Determine the solution of the differential equation.

A:

Q: y = C1+ C2cosx + C3sinx %3D

A: The given equation is, y=c1+c2cosx+c3sinx⋯⋯⋯⋯1 Differentiating with respect to x,…

Q: (x*y- xy")(xdy + ydx) + dy = 2xdx

A: To solve the differential equation we use some special form