Given that y, (x) = x² and y2 (x) : = x are two fundamental solutions of the differential equation z²y" (x) – 2xy' (æ)+ 2y (x) = x, x > 0. If the particular solution of the given differential equation is searched in the form Yp (x) = v1 (x) Yı (x) + v½ (x) y2 (æ) by the method of variation of parameters, what is v, (x) ? Select one: V1 (x) O v1 (x) = - o th (x) = 글 (т) V1 (1) =

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: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

A:

Q: 2. Which is the linear differential equation? (a) y' + ycosx = sinx (b) y" = (2 + (y)2)/2 (c) yt" =…

A: 1. In Linear differential equations change in output is directly proportional to change in input. 2.…

Q: Find a first order differential equation for which y2 sin(xy) + (2xe)cos(x)) = 3 is an implicit…

A:

Q: (a) y" +6y' +8y=8e-²x

A:

Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

A:

Q: What is the general real solution of the differential equation x3) – x(1} - 2x = 0 (the given…

A: The solution of linear homogeneous differential equation is defined by the roots of its…

Q: Now find the solution of the differential equation that satisfies the conditions y(0) = 4 and y' (0)…

A:

Q: yl" +4y/+3y =1

A: we will solve this by using Laplace transformation. Consider the equation y''+4y'+3y=1. Take Laplace…

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: 3( 1+x2 )y' = 2xy( y3-1) Find the general solution by determining the type of differential equation.

A:

Q: Obtain the particular solution of (3x2-2y2)y'=2xy; when x=0. y=-1

A:

Q: Consider the differential equation (x²-1) y"- 6x y¹+12y=0 (where prime denotes the derivative with…

A:

Q: The general solution to the differential equation y"+10y'+(e²x-7)y=0 1 y=f(x)(C₁ Ja (g(x)) + C₂ Ya…

A: The Bessel differential equationx2y″+xy′+(x2−n2)y=0When n is integer .The general solution of this…

Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

A:

Q: The solution of the differential equation (x³ + 3xy?)dx+ (y³+3x²y)dy=D0 is

A: The given differential equation is x3+3xy2dx+y3+3x2ydy=0. Comparing the given differential equation…

Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

A: To verify that the function y=x+2√x+5 is a solution the given differential equation.

Q: Determine the second solution and the general solution of the differential equation (1-2x-x²)y" +…

A: Step 1: To solve the given second-order linear homogeneous differential equation using the order…

Q: 3( 1+x2 )y' = 2xy( y3-1) Find the general solution by determining the type of differential equation.

A: According to the given information, it is required to find the general solution.

Q: Use the substitution t = x - xo to solve the given differential equation. (x + 6)2y" + (x + 6)y' + y…

A:

Q: 3. a) Use the substitution u = -x+3y to solve the differential equation. -x+3y)y'= 1 b) Clearly…

A: After substitutions, separate du and dx.

Q: (y-x)=y-x+ 2; y=x+2√x+4 When y=x+2√x+4. Y' = Thus, in terms of x, (y-x)y' = y-x+2= Since the left…

A: If  y=x+2x+4 is a solution of (y-x)y'=y-x+2 then it must satisfy it.

Q: 'X (y+2) y² = In x + 1 g(1) = -1 yCD: find the differential équation.

A: Let us consider the differential equation of the form dydx=f(x)g(y) The differential equation will…

Q: If the function y=x³ is a solution of the differential equation y''-2y'+y =q(x), then a) Determine…

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.