1. Use the procedures developed in this chapter to find the
general solution of the differential equation.
a.) (Let x be the independent variable.)
y''' − 2y'' = 12
b.) 20x2y'' + 21xy' − y = 0
c.) x2y'' − 6xy' + 10y = −2x4 +
3x2
d.) Solve the given differential equation subject to the
indicated conditions. y'' − 4y = x + sin x, y(0) = 3, y'(0) = 4
e.) Solve the given differential equation subject to
the indicated...
Use the one solution given below to find the general solution of
the differential equation below by reduction of order method:
(1 - 2x) y'' + 2y' + (2x - 3) y = 0
One solution: y1 = ex
Partial Differential Equations
(a) Find the general solution to the given partial differential
equation and (b) use it to find the solution satisfying the given
initial data.
Exercise 1. 2∂u ∂x − ∂u ∂y = (x + y)u
u(x, x) = e −x 2
Exercise 2. ∂u ∂x = −(2x + y) ∂u ∂y
u(0, y) = 1 + y 2
Exercise 3. y ∂u ∂x + x ∂u ∂y = 0
u(x, 0) = x 4
Exercise 4. ∂u...
For the following differential equation
y'' + 9y = sec3x,
(a) Find the general solution yh, for the
corresponding homogeneous ODE.
(b) Use the variation of parameters to find the
particular solution yp.