Solving a Second Order Differential Equation

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Anthony Mullins
Anthony Mullins 2021-1-29
编辑： James Tursa 2021-1-29

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回答（2 个）

Steven Lord
Steven Lord 2021-1-29
Ran in:
syms x t y(t)
dx = diff(x, t)
dx = 
0
dy = diff(y, t)
dy(t) = 
x is not a function of t so its derivative with respect to t is 0.
y is a function of t so its derivative with respect to t is not 0. [It could be, if you substituted a constant into dy for y, but it's not always zero.]
dyForConstant = subs(dy, y, 5)
dyForConstant(t) = 
0
dyForNonconstant = subs(dy, y, sin(t))
dyForNonconstant(t) = 
  1 个评论
Anthony Mullins
Anthony Mullins 2021-1-29
编辑：Anthony Mullins 2021-1-29
@Steven Lord I was getting the same error with the y instead of x. The error said there is no differential equations found. So I switched them not knowing that dx = 0. But I still cannot solve this.
I get this when I remove the % for the cond

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James Tursa
James Tursa 2021-1-29
编辑：James Tursa 2021-1-29
Here is what I get:
>> syms y(t)
>> eqn = 4*diff(y,t,2)+32*diff(y,t)+24*y^3 == 192;
>> Dy = diff(y,t);
>> cond = [y(0)==1.5, Dy(0)==0];
>> ySol(t) = dsolve(eqn,cond)
Warning: Unable to find symbolic solution.
> In dsolve (line 216)
ySol(t) =
[ empty sym ]
Maybe not surprising that it can't find a symbolic solution given the y^3 term. So you could use a numeric solver instead. E.g.,
f = @(t,y) [y(2);(192 - 32*y(2) - 24*y(1)^3)/4];
[t,y] = ode45(f,[0 10],[1.5;0]);
plot(t,y(:,1)); grid on

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