# How do you find a Power Series solution of a differential equation?

By matching each coefficients, #(n+2)(n+1)c_{n+2}=c_n Rightarrow c_{n+2}=c_n/{(n+2)(n+1)}#

By signing up, you agree to our Terms of Service and Privacy Policy

To find a power series solution of a differential equation, follow these steps:

- Write the differential equation as a power series.
- Expand the functions involved in the equation as power series.
- Substitute the power series expansions into the original differential equation.
- Equate coefficients of like powers of the independent variable.
- Solve the resulting recurrence relations to find the coefficients of the power series solution.
- Write the power series solution with the determined coefficients.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the interval of convergence #Sigma n3^nx^n# from #n=[0,oo)#?
- How do you do the Taylor series expansion for #f(x)=x/(1-x)# at a=1?
- How do you find the power series for #f'(x)# and #int f(t)dt# from [0,x] given the function #f(x)=Sigma (n+1)/nx^n# from #n=[1,oo)#?
- What is the coefficient of x^2 in the Taylor series for #(1+x)^-2# about a=0?
- How can I show that #lim_(x->0)(1-cos(x^2))/(xsin(x^3))=1/2# using the Maclaurin series?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7