This preview shows page 1. Sign up to view the full content.
Unformatted text preview: uations
Ax = b .
5
2
x2 + x3 = and x3 can be whatever.
3
3
5
2
x2 = − x3 +
3
3 • Example 3. Solve the equation 1
• so x1 − x3 =
3
1
x1 = x3 +
3 2
and
3
2
3 2/3
1
x = C −5 + 2/3
0
3 the general solution to
the homogeneous
problem one particular solution
to nonhomogeneous
problem Solutions to nonhomogeneous differential equations Solutions to nonhomogeneous differential equations
• To solve a nonhomogeneous differential equation: Solutions to nonhomogeneous differential equations
• To solve a nonhomogeneous differential equation:
1. Find the general solution to the associated homogeneous
problem, yh(t). Solutions to nonhomogeneous differential equations
• To solve a nonhomogeneous differential equation:
1. Find the general solution to the associated homogeneous
problem, yh(t). Solutions to nonhomogeneous differential equations
• To solve a nonhomogeneous differential equation:
1. Find the general solution to the associated homogeneous
problem, yh(t). Solutions to nonhomogeneous differential equations
• To solve a nonhomogeneous differential equation:
1. Find the general solution to the associated homogeneous
problem, yh(t).
ﬁrst order DE Solutions to nonhomogeneous differential equations
• To solve a nonhomogeneous differential equation:
1. Find the general solution to the associated homogeneous
problem, yh(t).
ﬁrst order DE second order DE Solutions to nonhomogeneous differential equations
• To solve a nonhomogeneous differential equation:
1. Find the general solution to the associated homogeneous
problem, yh(t).
ﬁrst order DE second order DE 2. Find a particular solution to the nonhomogeneous problem, yp(t). Solutions to nonhomogeneous differential equations
• To solve a nonhomogeneous differential equation:
1. Find the general solution to the associated homogeneous
problem, yh(t).
ﬁrst order DE second order DE 2. Find a particular solution to the nonhomogeneous problem, yp(t). Solutions to nonhomogeneous differential equations
• To solve a nonhomogeneous differential equation:
1. Find the general solution to the associated homogeneous
problem, yh(t).
ﬁrst order DE second order DE 2. Find a particular solution to the nonhomogeneous problem, yp(t). 3. The general solution to the nonhomogeneous problem is their
sum: y = yh + yp = C1 y1 + C2 y2 + yp Solutions to nonhomogeneous differential equations
• To solve a nonhomogeneous differential equation:
1. Find the general solution to the associated homogeneous
problem, yh(t).
ﬁrst order DE second order DE 2. Find a particular solution to the nonhomogeneous problem, yp(t). 3. The general solution to the nonhomogeneous problem is their
sum: y = yh + yp = C1 y1 + C2 y2 + yp Solutions to nonhomogeneous differential equations
• To solve a nonhomogeneous differential equation:
1. Find the general solution to the associated homogeneous
problem, yh(t).
ﬁrst order DE second order DE 2. Find a particular solution to the nonhomogeneous problem, yp(t). 3. The general solution to the nonhomogeneous problem is their
sum: y = yh + yp = C1 y1 + C2 y2 + yp Solutions to nonhomogeneous differential equations
• To solve a nonhomogeneous differential equation:
1. Find the general solution to the associated homogeneous
problem, yh(t).
ﬁrst order DE second order DE 2. Find a particular solution to the nonhomogeneous problem, yp(t). 3. The general solution to the nonhomogeneous problem is their
sum: y = yh + yp = C1 y1 + C2 y2 + yp
• For step 2, try “Method of undetermined coefﬁcients”... Method of undetermined coefﬁcients (3.5) Method of undetermined coefﬁcients (3.5)
• Example 4. Deﬁne the operator
general solution to L[y ] = e 2t L[y ] = y + 2y − 3y.
. That is, Find the y + 2y − 3y = e2t . Method of undetermined coef...
View
Full
Document
This note was uploaded on 02/12/2014 for the course MATH 256 taught by Professor Ericcytrynbaum during the Spring '13 term at The University of British Columbia.
 Spring '13
 EricCytrynbaum
 Differential Equations, Geometry, Equations

Click to edit the document details