Reduction of order

Reduction of order is a technique in mathematics for solving second-order linear ordinary differential equations. It is employed when one solution y 1 ( x ) {displaystyle y_{1}(x)} is known and a second linearly independent solution y 2 ( x ) {displaystyle y_{2}(x)} is desired. The method also applies to n-th order equations. In this case the ansatz will yield an (n-1)-th order equation for v {displaystyle v} . Reduction of order is a technique in mathematics for solving second-order linear ordinary differential equations. It is employed when one solution y 1 ( x ) {displaystyle y_{1}(x)} is known and a second linearly independent solution y 2 ( x ) {displaystyle y_{2}(x)} is desired. The method also applies to n-th order equations. In this case the ansatz will yield an (n-1)-th order equation for v {displaystyle v} .