clc; clear; close all;
%% Част 1: Намерете общото решение на диференциалното уравнение
syms y(x)
ode
= diff
(y
, x
) == 3*y
+ 3*x^
3*exp(-4*x
) - 1;sol = dsolve(ode);
disp('Общото решение на диференциалното уравнение:');
disp(sol);
%% Част 2: Векторно поле
[xGrid, yGrid] = meshgrid(linspace(-4,4,20), linspace(-4,4,20));
dy
= 3*yGrid
+ 3*xGrid
.^
3 .* exp(-4*xGrid
) - 1;dx = ones(size(dy)); % dx/dx = 1
figure;
quiver(xGrid, yGrid, dx, dy, 'r');
xlabel('x'); ylabel('y'); title('Векторно поле');
axis([-4 4 -4 4]);
grid on;
%% Част 3: Интегрални криви
hold on;
for y0 = -3:1:3
[x
, ySol
] = ode45
(@(x
,y
) 3*y
+ 3*x^
3*exp(-4*x
) - 1, [-4, 4], y0
); plot(x, ySol, 'b', 'LineWidth', 1.5);
legend('Векторно поле', 'Интегрални криви');
hold off;
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
clc; clear; close all;
%% Част 1: Намерете общото решение на диференциалното уравнение
syms y(x)
ode = diff(y, x) == 3*y + 3*x^3*exp(-4*x) - 1;
sol = dsolve(ode);
disp('Общото решение на диференциалното уравнение:');
disp(sol);
%% Част 2: Векторно поле
[xGrid, yGrid] = meshgrid(linspace(-4,4,20), linspace(-4,4,20));
dy = 3*yGrid + 3*xGrid.^3 .* exp(-4*xGrid) - 1;
dx = ones(size(dy)); % dx/dx = 1
figure;
quiver(xGrid, yGrid, dx, dy, 'r');
xlabel('x'); ylabel('y'); title('Векторно поле');
axis([-4 4 -4 4]);
grid on;
%% Част 3: Интегрални криви
hold on;
for y0 = -3:1:3
[x, ySol] = ode45(@(x,y) 3*y + 3*x^3*exp(-4*x) - 1, [-4, 4], y0);
plot(x, ySol, 'b', 'LineWidth', 1.5);
end
legend('Векторно поле', 'Интегрални криви');
hold off;