- #1
hedlund
- 34
- 0
I'm finding this diff equation hard
[tex] y'' + \ln{y} = yx [/tex]
How do I solve it?
[tex] y'' + \ln{y} = yx [/tex]
How do I solve it?
No, that won't work: this is not a linear equation. The right hand side is ln(y), NOT ln(x)!Dr Transport said:rearrange: [tex] y'' - xy = -\ln(y) [/tex], solve the homogeneous equation for [tex] y [/tex] then use those solutions as an integrating factor, or Green's function to solve the equation.
dt
arildno said:Step 5) is wrong hedlund
From 4), we have:
ln(y''+ln(y))-ln(y)=ln(y''/y+ln(y)/y)
As I'm sure you agree with..
A differential equation is an equation that involves an unknown function and its derivatives. It describes the relationship between a function and its rate of change.
To solve a differential equation, you need to find the function that satisfies the equation. This can be done through various methods such as separation of variables, substitution, or using specific formulas for different types of equations.
The order of a differential equation is the highest derivative present in the equation. For example, a first-order differential equation contains only first derivatives, while a second-order differential equation contains second derivatives.
The symbol y'' represents the second derivative of the function y with respect to the independent variable x. The symbol ln(y) represents the natural logarithm of the function y. The symbol yx represents the product of the function y and the independent variable x.
No, not all differential equations can be solved analytically. Some equations are too complex and do not have a closed-form solution. In these cases, numerical methods or approximations may be used to find an approximate solution.