Solving nth Order Differential Equations

Category: Differential Equations, Integral Calculus, Trigonometry

"Published in Newark, California, USA"

Find the general solution for

Solution:

Consider the given equation above

The given equation is a 4th Order Differential Equation because the fourth derivative of y with respect to x is involved. We can rewrite the given equation as follows

Multiply both sides of the equation by dx, we have

Integrate on both sides of the equation, we have 

Rewrite the above equation as follows 

Multiply both sides of the equation by dx, we have 

Integrate on both sides of the equation, we have 

Rewrite the above equation as follows 

Multiply both sides of the equation by dx, we have 

Multiply both sides of the equation by dx, we have 

where

Solving 2nd Order Differential Equations, 4

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 

  

Consider

If

then

If 

then

Hence, by integration by parts

Substitute the above equation to the original equation, 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