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

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Sheila Mae Soriano
评论： Sheila Mae Soriano 2021-9-13
How to solve y''+y'-y=x+1 using y(0)=1 and y'(0)=0. Plot the solution.
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Walter Roberson
Walter Roberson 2021-9-9
Ran in:
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;

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采纳的回答

Walter Roberson
Walter Roberson 2021-9-9
Ran in:
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])

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