A Particular Solution of a differential equation is a solution obtained from the General Solution by assigning specific values to the arbitrary constants.
Lets do the first one. y″−3y′−18y=x2e−2x. The homogeneous solution is: yh(x)=c1e−3x+c2e6x. Next, lets do the calculations for the particular solution ...
Find the particular solution of the differential equation which satisfies the given inital condition: First, we need to integrate both sides, which gives us the general solution: Now, we apply the initial conditions (x = 1, y = 4) and solve for C, which we …
The nonhomogeneous differential equation of this type has the form ... In both cases, a choice for the particular solution should match the structure of the ...
17.02.2013 · This video provides examples of how to determine the form of the particular solution to a linear second order nonhomogeneous differential equation when terms...
25.03.2017 · Form of a particular solution with undetermined coefficients, particular solution for a non-homogeneous differential equation, second order non-homogeneous l...
To find a particular solution to the nonhomogeneous equation we guess that it has to have the form yp(t) = Aet, where A is a constant to be determined.
Solution: The general form of solution is = A. Z r Now putting this solution on L.H.S of equation (i), we get = A Z r+2 -3AZ r+1 +2AZ r = (Z 2 -3Z+2) A Z r .........equation (ii) Equating equation (ii) with R.H.S of equation (i), we get (Z 2 -3Z+2)A=1 A = (Z≠1, Z≠2) Therefore, the particular solution is
03.06.2018 · Example 6 Write down the form of the particular solution to y′′ +p(t)y′ +q(t)y = g(t) y ″ + p ( t) y ′ + q ( t) y = g ( t) g(t) = 16e7tsin(10t) g ( t) = 16 e 7 t sin ( 10 t) g(t) = (9t2 −103t)cost g ( t) = ( 9 t 2 − 103 t) cos t g(t) = −e−2t(3−5t)cos(9t) g ( t) = − e − 2 t ( 3 − 5 t) cos ( 9 t) Show All Solutions Hide All Solutions