gistfile1.cpp

		void rk4()
		{
			label_t->Text = "t = " + t.ToString("F2");

			label_x->Text = "x = " + x.ToString("F2");
			label_y->Text = "y = " + fy(x).ToString("F2");
			label_v->Text = "v = " + v.ToString("F2");

			E = v*v*0.5 + fy(x);
			label_E->Text = "E = " + E.ToString("F2");

		t = t + dt;

		x=xk;
		v=vk;

		k1x = dt*v;
		k1v = dt*fv(x, v, t);

		k2x = dt*(v + k1v / 2);
		k2v = dt*fv(x + k1x / 2, v + k1v / 2, t + dt / 2);

		k3x = dt*(v + k2v / 2);
		k3v = dt*fv(x + k2x / 2, v + k2v / 2, t + dt / 2);

		k4x = dt*(v + k3v);
		k4v = dt*fv(x + k3x, v + k3v, t + dt);

		xk = x + u * (k1x + 2 * k2x + 2 * k3x + k4x);
		vk = v + u * (k1v + 2 * k2v + 2 * k3v + k4v);
				
			pictureBox1->Invalidate();
			pictureBox2->Invalidate();
			pictureBox3->Invalidate();
		
		}

private: System::Void pictureBox2_Paint(System::Object^  sender, System::Windows::Forms::PaintEventArgs^  e) 
	{
				 e->Graphics->DrawImage(bitmapa2, 0, 0);
				 Graphics^ grafika2 = Graphics::FromImage(bitmapa2);
				 Graphics^ grafika21 = e->Graphics;
				 System::Drawing::Font^ czcionka = gcnew System::Drawing::Font(System::Drawing::FontFamily::GenericSansSerif, 10, FontStyle::Regular);

		//		 grafika2->Clear(Color::White);

				 Pen^ pen1 = gcnew Pen(Color::Gray);
				 Pen^ pen2 = gcnew Pen(Color::Black);
				 Pen^ pen3 = gcnew Pen(Color::Gray);
				 SolidBrush^ brush1 = gcnew SolidBrush(System::Drawing::Color::Red);
				 SolidBrush^ brush2 = gcnew SolidBrush(System::Drawing::Color::Gray);

				 // układ współrzędnych

				 pen1->Width = 2;
				 
				 grafika2->DrawLine(pen1, eX2(Xp), eV(0.0), eX2(Xk), eV(0.0));
				 grafika2->DrawLine(pen1, eX2(0.0), eV(Vp), eX2(0.0), eV(Vk));

				 // trajektoria
				 
				 pen2->Width = 1;
				 grafika2->DrawLine(pen2, eX2(x), eV(v), eX2(xk), eV(vk));	

				 // siatka

				 pen3->Width = 0.5;
				 pen3->DashStyle = DashStyle::Dash;

				 for (int i = Vp; i<Vk + 1; i++)
					 grafika2->DrawLine(pen3, eX2(Xp), eV(i), eX2(Xk), eV(i));

				 for (int i = Xp; i<Xk + 1; i++)
					 grafika2->DrawLine(pen3, eX2(i), eV(Vp), eX2(i), eV(Vk));

				 // opis osi

				for (int i = Xp; i<Xk; i++)
					grafika2->DrawString(i.ToString(), czcionka, brush2, eX2(i), eV(0));

				for (int i = Vp; i<Vk; i++)
					grafika2->DrawString(i.ToString(), czcionka, brush2, eX2(0), eV(i));
				
				// rysowanie bitmapy

				 e->Graphics->DrawImage(bitmapa2, 0, 0);	

				 // kulka

				 grafika21->FillEllipse(brush1, eX2(x) - 4, eV(v) - 4, 8, 8);
	}