Verify that the given functions y1 and y2 satisfy the corresponding homogeneous equation; then find a particular solution of the given nonhomogeneous equation. x2y'' − 3xy' + 4y = 11x2 ln x, x > 0; y1(x) = x2, y2(x) = x2 ln x

Therefore the particular solution of the given differential equation is  

Step-by-step explanation:

The given ordinary differential equation is

If y₁(x) =x² is a solution of ODE then it will be satisfy the ODE

y₁'(x)= 2x and y₁"(x)=2

Putting the value of y₁'(x) and y₁"(x) in x²y"-3xy'+4y=0 we get

x².2-3x.2x+4x²= 2x²-6x²+4x²=0

Therefore y₁(x)  is a solution of the given differential equation.

Again,

y₂(x) =(x²ln x ) is a solution of ODE then it will be satisfy the ODE.

= 3+2 ln x

Putting the value of y₂'(x) and y₂"(x) in x²y"-3xy'+4y=0 we get

=0

Therefore  y₂(x) is a solution of  the given differential equation.

The wronskian of y₁(x) and  y₂(x)  is

            =x²(2x ln x+x)-x²ln x(2x)

            =2x³ ln x +x³ - 2x³ln x

            =x³≠0

Here

The particular solution is

                              Let ln x  =u  

Therefore the particular solution of the given differential equation is  

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8.   4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!

175

step-by-step explanation:

2 inches x 10 miles = 200 miles - 3 inches = 175