Differential Equation Homework cant rotate it dont know why

Differential Equation Homework

(can\'t rotate it, don\'t know why)

Undetermined Coefficients Let us assume that y1,y2.....yn forms a set of linearly independent solutions for the homogeneous equation y^(n)+an-1y^(n 1)+......+a1y^\'+a0y=0 when one is looking for a particular solution to the non-homogeneous equation y(n)+ an-1y^(n-1)+ ...+ a1y^\'+ a0y= f(x), the method of undetermined coefficients provides an algorithm for nice enough functions f(x). We distinguish two situations: If no term appearing either in /(x) or any of the derivatives of f(x) is a solution of the associated homogeneous differential equation (notice that this is the same as saying that none of the y(s can be terms in any of the derivatives of f(x)), then one can try a linear combination of all the linearly independent terms within f(x) and its derivatives as a particular solution. Practice problems. Consider the equationy^\'\'+6y^\'-7y = sinx. Find y1(x) and y2(x), the fundamental solutions of the associated homogeneous equation. Find all the derivatives of f(x))= sin a: and check whether any of them satisfies the associated homogeneous equation. Try to find a particular solution of the type Yp(x)= Asinx + Bcosx. Find the general solution of the original equation. Consider the equation y^\'\'+6y^\'-7y= -21x3 + 2. Find yi^(x)and 2/2(2), the fundamental solutions of the associated homogeneous equation. Find all the derivatives of f(x) = -21ar3 + 2 and check whether any of them satisfies the associated homogeneous equation. Try to find a particular solution of the type yp(x)= AX^3bx^2+ cx+d Find the general solution of the original equation. Consider the equation y^\'\'+6y^\'-7y = sinx-2x^3.Find the general solution of the original equation.

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