Solve for x given y and plot

I solved a 2nd Order Differential Equation for the following answer:

y= (2 * e^((2*x)/3)) - ((7*x*e^((2x)/3))/3)

Now, given y=-4, I want to plot and find the value of x when the plot first crosses y=-4.

Answer 1

[Star Strider]

Depending on what you wan, either use fzero or interp1 —

y = @(x) (2 * exp((2*x)/3)) - ((7*x.*exp((2*x)/3))/3);
x = linspace(0, 2);

yq = -4;
xq = fzero(@(x) y(x) + 4, 1)

xq = 1.4914

xq = interp1(y(x), x, -4)

xq = 1.4914

figure
plot(x, y(x))
hold on
plot(xq, yq, 'r+')
hold off
grid
xlabel('x')
ylabel('y')

.