Solving 2nd Order Differential Equations, 2

Category: Differential Equations, Integral Calculus

"Published in Newark, California, USA"

Find the general solution for

Solution:

Consider the given equation above

The given equation is a 2nd Order Differential Equation because the second derivative of y with respect to x is involved. We can rewrite given equation as follows

Multiply both sides of the equation by dx, we have 

Integrate on both sides of the equation, we have 

Multiply both sides of the equation by dx, we have 

Multiply both sides of the equation by dx, we have 

Integrate on both sides of the equation, we have 

Consider

If 

then

If 

then

Hence, by integration by parts

Substitute the above equation to the original equation, we have

where

 

Definite Integral - Algebraic Functions, Powers, 10

Category: Integral Calculus, Algebra

"Published in Newark, California, USA"

Evaluate

Solution:

Consider the given equation above

The first thing that we have to do is to integrate the given equation above, we have

The constant of integration is not included in the definite integral. Substitute the values of upper and lower limits to the above equation, we have

Therefore,

 

Definite Integral - Algebraic Functions, Powers, 9

Category: Integral Calculus, Algebra

"Published in Newark, California, USA"

Evaluate

Solution:

Consider the given equation above

The first thing that we have to do is to square the binomial, we have

Next, integrate the resulting equation, we have

The constant of integration is not included in the definite integral. Substitute the values of upper and lower limits to the above equation, we have

Therefore,