Differential Equations Answers

1. y'' + 4y' + 7y = 0      ans, y= e^-2x(c₁cosx+c₂sinx)
2. 2y'' - 7y' + 3y = 0     ans, y=c₁e^3x+c₂e^1/2x

Evaluate the following functions in differential operator form.

1. D(x²+2x-3) Ans. (2x+2)
2. D²(xe^3x-e^4x) Ans. 9xe^3x+6e^3x-16e^4x

Solve the following differential equations in series.

x²d²y/dx + xdy/dx +(x²-4)y=0

reduce the following equation onto canonical form

u_x+2xyu_y=x

2x^ 3 y^ prime =y(y^ 2 +3x^ 2 )

Solve differential equation

(D^3-6D’D+11D’^2D-6D’)z=cos(2x+y)+e^(2x+y)-y

find the general solution of the homogeneous linear equations

1.(2D²-5D-3)y=0

2. (9D²-6D+1)y=0

3. (D⁴-2D²)y=0

4. (D⁵+8D³+16D)y=0

5. (D³+8)y=0

Find two members of the family of solution in problem 5 that satisfy the initial condition y(0)=0, y'(0)=0.

y''-10y'+25y=0 find general solution of the given second order differential equation.