The solution of the differential equation x'y" + 3xy' + 6y = 0 (x > 0) is the function y(x) = C, y;(x) + C2 y:(x). Find y,(x) and y:(x). Also, find the constants C, and C; if y(1) = - 1, y(1) = 2. O A. y,) = x' cos (V5 In(x), y;0«) = x' sin (V3 In(x), c, - - 1, C, = O B. y,() = x' cos (V3 In(x), y:0x) = x' sin (V3 In(x), c, - - 1, G; = - O C. y,(x) = x cos (V5 In(x)), y:(x) = x sin(v3 In(x)), C, = - 1, C; = - O D. y,(x) = x cos (V5 In(x»), y,x) = x sin (V3 In(x), C, = - 1, C; =

Q: y = (C₁ + C₂x) eª + sinx+x²; y" - 2y' + y = −2 cos x + x² − 4x + 2

A: Here we find the first and second derivatives of given solution and then put in the left hand side…

Q: Show that if P(x) #0 the differential equation y' + p(x)y = f(x) is not exact differential equation.…

A: y' + p(x)y = f(x) can be written in the appropriate form dydx + p(x)y = f(x)  ⇒dy +p(x)y dx = f(x)…

Q: Solve the differential equation by variation of parameters, subject to the initial conditions y(0) -…

A: It is given that the differential equation is 2y''+y'-y=x+5 The auxiliary equation is 2r2+r-1=0…

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A:

Q: Problem 6. Consider a linear operator L: R³ R³ given by L(x, y, z) = (2z, y + 3x, 2x - z) for all…

A:

Q: y' + (=) y = xy²

A:

Q: Find the general solution af the equation, y' = x(1- y).

A:

Q: y' + }xy = sin(x 4e¤2 y3 1

A:

Q: Find the solution to the differential equation: cosxcos ydx + sin x sin ydy 0 a. cos x = C'siny O b.…

A:

Q: (x-xo)²y" + (x − xo)p(x)y' + g(x)y = 0 (3) - ch regular singular point of the equation. Identify the…

A: We have to write in the form

Q: y = xy' – 2(y')² + 3

A:

Q: of y' = x²/(y + 1)?

A:

Q: What is the differential equation of all parabolas with axis parallel to the y-axis?

A:

Q: sy(

A:

Q: Find the solution for this second ODE y(0) = 1, y'(0) = 1

A:

Q: A solution of the Ordinary Differential Equation x?y'' - 2xy' + (x² + 2) y = 0, x > 0 is defined by…

A: 4th option is correct. y_p= xcos(x)

Q: Find the value of a for which the equation y''+a^2y=0 has non trivial solution such that y(0)=y(pi)…

A: Since we have that                  y''+a2y=0                y(0)=y(π)   and y'(0)=y'(π) Then…

Q: solve the below differential equation: y''2+y'y'''=(y'/x)2

A: Given the differential equation  y''2+y'y'''=y'x2 To solve this differential equation.

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.