I solved it and got general solution of y=c1e^5x+c2xe5x and the derivative is y'=c1(5e^5x)+c2(5xe^5x)axmls said:We have to see what you're doing to know what you're doing wrong.
Ohmygodd! You are right I did a silly mistake!axmls said:You need to use the product rule on the second term: [tex](x e^{5x})' = x' e^{5x} + x (e^{5x})' = e^{5x} + 5x e^{5x}.[/tex]
Also, as a side note, it's advised that you use the homework section for any difficulties you're having in homework next time you have a question.
An ODE, or ordinary differential equation, is a mathematical equation that describes the relationship between a function and its derivatives. It involves one or more independent variables and one or more dependent variables.
Solving an ODE means finding the function that satisfies the equation, as well as any given initial conditions. In other words, it is finding the relationship between the dependent and independent variables that satisfies the equation.
An initial condition is the value of the dependent variable at a specific point in the independent variable. It is often denoted as y(0), where 0 is the initial value of the independent variable.
To solve an ODE with initial condition, you first need to determine the type of ODE and its order. Then, you can use various techniques such as separation of variables, substitution, or integrating factors to find the general solution. Finally, you can use the initial condition to find the specific solution that satisfies the given condition.
Solving ODEs is important in many fields of science and engineering. It allows us to model and understand real-world phenomena, such as the motion of objects, growth of populations, and chemical reactions. ODEs also play a crucial role in developing mathematical models for predicting and analyzing complex systems.