Question 1

Solve the boundary-value problem, if possible. $y ^ { \prime \prime } + 16 y ^ { \prime } + 64 y = 0 , y ( 0 ) = 0 , y ( 1 ) = 4$

Accepted Answer

A)  $y ( x ) = 4 x e ^ { ( - 8 x + 8 ) }$ 
B)  $y ( x ) = 4 e ^ { ( - 8 x - 8 ) }$ 
C)  $y ( x ) = 4 x e ^ { ( - 8 x - 8 ) }$ 
D)  $y ( x ) = 8 x e ^ { ( - 4 x + 4 ) }$ 
E)  No solution 
A)  $y ( x ) = 4 x e ^ { ( - 8 x + 8 ) }$ 
B)  $y ( x ) = 4 e ^ { ( - 8 x - 8 ) }$ 
C)  $y ( x ) = 4 x e ^ { ( - 8 x - 8 ) }$ 
D)  $y ( x ) = 8 x e ^ { ( - 4 x + 4 ) }$ 
E)  No solution

Question 2

Solve the differential equation. $y ^ { \prime \prime } - 2 y ^ { \prime } = e ^ { 2 x }$

Accepted Answer

The answer of Solve the differential equation. \(y ^ {...

Question 3

Solve the initial-value problem. $2 y ^ { \prime \prime } + 19 y ^ { \prime } + 24 y = 0 , y ( 0 ) = 0 , y ^ { \prime } ( 0 ) = 6$

Accepted Answer

The answer of Solve the initial-value problem. \(2 y ^...

Solve the boundary-value problem, if possible. $y ^ { \prime \prime } + 16 y ^ { \prime } + 64 y = 0 , y ( 0 ) = 0 , y ( 1 ) = 4$

Solve the differential equation. $y ^ { \prime \prime } - 2 y ^ { \prime } = e ^ { 2 x }$

Solve the initial-value problem. $2 y ^ { \prime \prime } + 19 y ^ { \prime } + 24 y = 0 , y ( 0 ) = 0 , y ^ { \prime } ( 0 ) = 6$

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Final Exam

Filters

Exam 17: Second-Order Differential Equations

Solve the boundary-value problem, if possible. y′′+16y′+64y=0,y(0)=0,y(1)=4y ^ { \prime \prime } + 16 y ^ { \prime } + 64 y = 0 , y ( 0 ) = 0 , y ( 1 ) = 4y′′+16y′+64y=0,y(0)=0,y(1)=4

Solve the differential equation. y′′−2y′=e2xy ^ { \prime \prime } - 2 y ^ { \prime } = e ^ { 2 x }y′′−2y′=e2x

Solve the initial-value problem. 2y′′+19y′+24y=0,y(0)=0,y′(0)=62 y ^ { \prime \prime } + 19 y ^ { \prime } + 24 y = 0 , y ( 0 ) = 0 , y ^ { \prime } ( 0 ) = 62y′′+19y′+24y=0,y(0)=0,y′(0)=6

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Final Exam

Filters

Solve the boundary-value problem, if possible. $y ^ { \prime \prime } + 16 y ^ { \prime } + 64 y = 0 , y ( 0 ) = 0 , y ( 1 ) = 4$

Solve the differential equation. $y ^ { \prime \prime } - 2 y ^ { \prime } = e ^ { 2 x }$

Solve the initial-value problem. $2 y ^ { \prime \prime } + 19 y ^ { \prime } + 24 y = 0 , y ( 0 ) = 0 , y ^ { \prime } ( 0 ) = 6$