Solving ordinary differential equations using power series page 15 hence the resulting solution of legendres differential equation 49 is called the legendre polynomial of degree and is . Section 1 2 direction fields this topic is given its own section for a couple of reasons first understanding direction fields and what they tell us about a differential equation and its solution is important and can be introduced without any knowledge of how to solve a differential equation and so can be done here before we get into solving them. We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations the exp function method is extended to solve fractional partial differential equations in the sense of the modified riemann liouville derivative we apply the exp function method to the time fractional sharma tasso olver equation the space . Differential equations are very common in physics and mathematics without their calculation can not solve many problems especially in mathematical physics one of the stages of solutions of differential equations is integration of functions there are standard methods for the solution of differential equations should be brought to the form . In this section we discuss the solution to homogeneous linear second order differential equations ay by c 0 in which the roots of the characteristic polynomial ar2 br c 0 are complex roots we will also derive from the complex roots the standard solution that is typically used in this case that will not involve complex numbers
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