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The particular solution of differential equation can be easily identified, as it does not have any arbitrary constants. The solutions y = 3x + 3, y = x2 + 11x + 7, are the examples of particular solution of differential equation.
- How do you find the complementary and particular solution of a differential equation?
- How many particular solutions does a differential equation have?
- How to find particular solution of 2nd order differential equation?
How do you find the complementary and particular solution of a differential equation?
Note: A complementary function is the general solution of a homogeneous, linear differential equation. To find the complementary function we must make use of the following property. ycf(x) = Ay1(x) + By2(x) where A, B are constants.
How many particular solutions does a differential equation have?
A differential equation has infinitely many solutions. For example, the general solution to the differential equation y'=2x-2 is y=x2−2x+C y = x 2 − 2 x + C . 'C' has infinite values, so the differential equation has infinitely many solutions. But if the function passes through a point, it has only one solution.
How to find particular solution of 2nd order differential equation?
To find the solution of Non-Homogeneous Second Order Differential Equation y'' + py' + qy = f(x), the general solution is of the form y = yc + yp, where yc is the complementary solution of the homogeneous second order differential equation y'' + py' + qy = 0 and yp is the particular solution of the non-homogeneous ...
