Solving a Second Order Differential Equation

Answer 1

[Steven Lord]

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) = 

[Anthony Mullins]

@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

Answer 2

[James Tursa]

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