Question

solve the following differential equations (i) (d2+2 d+2)y=sinhx​

Answer 1

Answer:

y = C1e^x + C2e^x + (x/2) cosh (x)

Step-by-step explanation:

For the equation (D^2 - 1)y = sinh(x) the characteristic polynomium is

m^2 - 1 =0 . Roots 1 , - 1.The solution to the homogeneous part of the

equation is yh = C1e^x + C2e^-x =(C1+C2)cosh(x) + (C1-C2)sinh(x) . The function

sinh(x) is solution of the equation with multiplicity 1.Then ,the method of

undetermined coefficients requires a particular integral

yp =x( Acosh(x) + Bsinh(x) ).Substituting in the equation obtain A =1/2 , B=0 .

Then yp =(1/2)xcosh(x) and the solution of the equation is

y =C1e^x + C2e^-x + (x/2)cosh(x).