How do i solve a non homogenous diff equation without dsolve? I have done the code for the complimentary function pls help me with the particular solution part

clc

syms t m k1 k2

a=input(' Enter the coefficient of D2y:');

b=input(' Enter the coefficient of Dy:');

c=input(' Enter the coeeficent of y:');

cq=a*m^2+b*m+c;

r=solve(cq)

if imag(r)~=0

disp('under damping')

y1=exp(real(r(1))*t)*cos(imag(r(1))*t);

y2=exp(real(r(1))*t)*sin(abs(imag(r(1)))*t);

elseif r(1)==r(2)

disp('Critical damping:')

y1=exp(r(1)*t);y2=t*exp(r(1)*t);

else

disp('over damping:')

y1=exp(r(1)*t);

y2=exp(r(2)*t);

end

disp(' The complimentary sol y_c is:')y_c=k1*y1+k2*y2

Answer 1

[Sameer]

Hi @Sid Nogueira

To find the particular solution of a non-homogeneous differential equation, you can use methods such as the method of undetermined coefficients or the method of variation of parameters.

1. Method of Undetermined Coefficients:

• Guess a form for the particular solution based on the non-homogeneous term.
• Substitute this guess into the differential equation to find unknown coefficients.

2. Method of Variation of Parameters:

• Use the complementary solution to construct a particular solution.
• Calculate specific integrals to find the parameters.

Hope this helps!