find general solution of y4y33y22y find general solution of

Solution

Consider the given equation

y^\'\'\'\' + y^\'\'\'- 3y^\'\'- 2y = 0

then the characteristic equation is r⁴ + r³ - 3r² - 2 = 0

The roots are -2.39687 , 1.52681 , -0.0649671 + 0.736405 i and -0.0649671 - 0.736405 i

Therefore , the general solution of the given equation is

y(x) = C₁ e^(-2.39687x) + C₂ e^(1.52681x) +e^{(-0.0649671x)}(C₃ cos( 0.736405x ) + C₄ sin( 0.736405x ) )