14. starptautiskā konference 2012 - Latvijas Jūras akadēmija

Proceedings of 14th International conference „Maritime Transport and Infrastructure - 2012”2 2 0 . (4)The appropriate roots of equation (4) are 1 ,2 j .The appropriate solution of equation (3) is stated using formula:y C1 costC2sint , (5)C1 un C 2are independent constants of integration. If right side of homogenous differentialequation is in special form:and P t un Q tftt e PtcostQt sin t(6)nn mare polinoms with the highest grade ( n and m) then particular solutioncan be acquired without using integration of non- defined coefficient method [3,4]. It necessary to takek max n,m and concurrence ofinto consideration the highest grade of polinoms j j 1 with rot of typical equation .If j then the particular solution of non – homogenous differential equation is writtenin form (6):y etNktcos t Mmktsin t. (7)If j then then the particular solution of non – homogenous differential equation iswritten in form : ty te N t cos t M t sin t. (8)Here N t un M tkkk k are polinoms with non – defined with grade k but with non – definedcoefficients. Coeficients are stated by replacing y in non – homogeneous differential equation with(solve also all y fluxions). It is also required that the identity is accomplished.In the right side of non - homogenous differential equation (1) one of the polinoms2P t highest grade is n = 0 but there is also no second polinom Q mt 0 therefore 20 ck max n,m and j 0 c j 0 .The particular solving of non – homogenous differential equation (1)y e0ty is written in form:a t bsinta cos t bsint0cosc 0 c 0 c 0c, (9)where is necessary to determine a0un b0.The function (9) must be imported in place of y into equation (1). By comparing coefficientsin equal functions two equations are acquired to compare and solve coefficients a0un b0. Then theparticular solution (9):y2 2 cy cos2 2 ct And the particular solution of (2) of equation (1):c(10)80