function hw2_246
clc
hw2_246_1
hw2_246_2

function hw2_246_1
    %% Part a
    syms y(t)
    dsolve('D2y + y*2 = 0');
    Dy = diff(y);
    sols = sym(zeros(11,1));
    for x = 1:10
      sols(x) = dsolve('D2y + y*2 = 0', y(0) == 0, Dy(0) == x/10);
    end
    figure
    hold on
    for x = 1:11
        ezplot(sols(x), [0,10])
    end
    hold off


    %% Part b
    syms y(t)
    Dy = diff(y);
    figure
    hold on
    ezplot(dsolve('D2y + Dy + y*2 = 0', y(0)== 0, Dy(0) == 2), [0 40])
    %ezplot(dsolve('D2y + Dy*2*sqrt(2) + y*2 = 0', y(0) == 2, Dy(0) == 2), [0 40])
    %second case doesn't want to work for whatever reason
    ezplot(dsolve('D2y + Dy*4 + y*2 = 0', y(0)== 2, Dy(0) == 2), [0 40])
    hold off

    %% Part c
    syms y(t)
    figure
    hold on
    ezplot('2*cos(sqrt(2)*t) + (sin(sqrt(2)*t)*sqrt(2))+(sin(7*t)-cos(sqrt(2)*t))/(-45)', [0, 40])
    ezplot('2*cos(sqrt(2)*t) + (sin(sqrt(2)*t)*sqrt(2))+t*sin(sqrt(2)*t)/(2*sqrt(2))', [0, 40])
    hold off
    %% Part d
    syms y(t)


function hw2_246_2
    hold on
    for k = 1:5
        m(k) = -2+(k-1);
        n(k) = -1+.5*(k-1);
        [t,x] = ode45('F',[-3,3],[m(k),n(k)]);
        plot(t,x(:,1))
    end
    hold off
function xp = F(t,x)
        xp = zeros(2,1);
        xp(1) = x(2);
        xp(2) = -t^3*x(2)-x(1);