Second order differential equation is that where the algebraic function is differentiated twice with respect to the given variable. It calculates the rate of change of the given function with respect to the change in the input.
Second order differential equation Calculator is a online tool to calculate the second order differential equation of any given algebraic function of the form y'' + py' + q = 0, where p and q are constant and gives the solutions instantly. It is a easy tool that reduces your effort of solving manually.

## Second Order Differential Equation Steps

Lets go through the way to solve second order differential equation:
Read the given problem and observe whether the given differential equation is of the form ay'' + py' + q = 0. Take it in form of a $\lambda^2$ + p $\lambda$ + q = 0

Take it as the quadratic equation and by taking out the value of a,b and c, solve for $\lambda$. You get two solutions $\lambda_1$ and $\lambda_2$.

If only real part exist in the solution express the answer in the form

y = c1 $e^{\lambda_1 x}$ + c2 $e^{\lambda_2 x}$

If the imaginary part also exist in the solution express the answer in the form

y = c1 $e^{i \lambda_1}$ + c2 $e^{ i \lambda_2 x}$

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