## Thursday, March 27, 2014

### Solving 2nd Order Differential Equations, 5

Category: Differential Equations, Integral Calculus, Algebra

"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

Since the degree of a variable for both numerator and denominator are the same, then we have to do the division of a polynomial with another polynomial. After the division, the right side of the equation becomes

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

Since the degree of a variable for both numerator and denominator are the same, then we have to do the division of a polynomial with another polynomial. After the division, the right side of the equation becomes

Substitute the above equation to the original equation, we have