Differential Equations Answers

y= e^mx

5(dy/dx) = 2y

The solution of (D – 3D²D' - 2DD'²) z = 0 is

Using the method of variation of parameters find the general solution of the differential equation x^2 y'' - 3xy' + 3y = 12x^4 given that y1 = x and y2 = x^3 are solutions of the corresponding homogenous equation.

Show that the general solution of the differential equation

4z'' - 4z' - 3z = cos2x takes the expression: z = c1e^(3x/2) + c2e^(-x/2) - (19/425)cos2x - (8/425)sin2x

dy/dx =x(ex² +2)/6y²

solve d²u/dt² =9d²u/dx² with 0《x《1

u(0,t)=0 , u(1,t)=0 , d u(x,0)/dt =0

u(x,0) = x 0《x《0.25

0.25 0.25《x《0.75

1-x 0.75《x《1

Find the integral of (y² -1 ) dx-2dy = 0

Find a linear differential operator that annihilates the given function. (Use D for the differential operator.)

cos 4x

A 2 kg mass is attached to a spring having spring constant 8N/m. The mass is placed in a surrounding medium with damping force numerically equal to 6 times the instantaneous velocity. The mass is initially released from the equilibrium position with an upward velocity of 2 m/s. Find the equation of motion.

Integrating Factors found by Inspection.

1. y(2xy + 1)dx − xdy = 0

2. y(x^4 − y^2)dx + x (x^4 + y^2)dy = 0

3. (x^3y^3 + 1)dx + x^4y^2dy = 0

4. y(x^2y^2 − 1)dx + x(x^2y^2 + 1)dy = 0

5. y(2x + y^2)dx + x(y^2 − x)dy = 0

6. y(3x^3 − x + y)dx + x^2(1 − x^2)dy = 0

7. y(3x^3 − x + y)dx + x^2(1 − x^2)dy = 0

8. y^2(1 − x^2)dx + x(x^2y + 2x + y) = 0