How to solve y''+y'-y=x+1 using y(0)=1 and y'(0)=0. Plot the solution.

How to solve y''+y'-y=x+1 using y(0)=1 and y'(0)=0. Plot the solution.

[Jan]

This sounds like a homework question. Please post, what you have tried so far and ask a specific question.

[Sheila Mae Soriano]

syms y(x)
Dy=diff(y);

ode=diff(y,x,2)+diff(y,x,1)-y==x+1;
cond1 = y(0)==1;
cond2=Dy(0)==0;

conds=[cond1 cond2];
sol=dsolve(ode,conds);
sol1=simplify(sol);

Am I doing it correctly?

[Walter Roberson]

syms y(x)
Dy=diff(y);

ode=diff(y,x,2)+diff(y,x,1)-y==x+1;
cond1 = y(0)==1;
cond2=Dy(0)==0;

conds=[cond1 cond2];
sol=dsolve(ode,conds);
sol1=simplify(sol);

sol1

sol1 = 

Looks okay.

As a matter of style, since you compute Dy already, it does not make sense to use diff(y,x,1) in the ode:

ode=diff(y,x,2)+Dy-y==x+1;

[Sheila Mae Soriano]

Thank you! Very helpful.

Answer 1

[Walter Roberson]

The below is deliberately different than your question (because your question looks like homework to me.)

syms y(x)
dy = diff(y)

dy(x) = 

d2y = diff(dy)

d2y(x) = 

eqn = 5*d2y + 7*dy - 9*y == x^2 - 11*x + 13

eqn(x) = 

ic = [y(0) == 2, dy(0) == 1]

ic = 

sol = dsolve([eqn, ic])

sol = 

fplot(sol, [0 10])