ODE with goniometric function

Hi, how can I solve and plot this ODE: 1*y''+23.25*(2.5*sin(x+1.5))*y'=0

there is my code:

eqn = '1*D2y+23.25*(2.5*sin(x+1.5))*D1y = 0';
inits = 'y(0)=0.7, Dy(0)=6.2';
y=dsolve(eqn,inits,'x')
ezplot(y, [-1 10])

Thank you so much

Answer 1

[Star Strider]

This works in R2018a, although it gives a ‘Warning’ about array inputs:

syms x y(x) 
D1y = diff(y);
D2y = diff(D1y);
eqn = D2y+23.25*(2.5*sin(x+1.5))*D1y == 0;
inits = [y(0)==0.7, D1y(0)==6.2];
y=dsolve(eqn,inits)
Y = matlabFunction(y)
ezplot(Y, [-1 10])

This assumes that ‘y’ is a function of ‘x’. If both ‘x’ and ‘y’ are functions of another variable, we need to know.

[Radek Zenkel]

I have R2015a and in this version it does not work :/

Error using symengine (line 59) The number of arguments in call of function 'int' is incorrect.

Error in sym/matlabFunction>mup2matcell (line 336) r = mup2mat(c{1});

[Star Strider]

In R2018a the matlabFunction call produces:

Y =

    function_handle with value:

      @(x)exp(cos(3.0./2.0).*(-4.65e2./8.0)).*integral(@(y)exp(cos(y+3.0./2.0).*(4.65e2./8.0)),0.0,x).*(3.1e1./5.0)+7.0./1.0e1

or, more conveniently:

Y = @(x) exp(cos(3.0./2.0).*(-4.65e2./8.0)).*integral(@(y)exp(cos(y+3.0./2.0).*(4.65e2./8.0)),0.0,x).*(3.1e1./5.0)+7.0./1.0e1;

however only this construction appears to work:

Y = @(x) exp(cos(3.0./2.0).*(-4.65e2./8.0)).*integral(@(y)exp(cos(y+3.0./2.0).*(4.65e2./8.0)),0.0,x,'ArrayValued',1).*(3.1e1./5.0)+7.0./1.0e1;
X = linspace(-1, 10);
Yv = arrayfun(Y, X);
figure
plot(X, Yv)
grid