MATLAB: How to solve the differential equation y(a-y)dy = udx/k calculusdifferential equationsintegrationnumerical solutionodeode23ode45 Here u, k and a are constants. Best Answer By integrating both sides of the equation:integral_{y=y0}^{y=y}y*(a-y) dy = (a*y^2/2 - y^3/3) - (a*y0^2/2 - y0^3/3)integral_{x=x0}^{x=x}u/k dx = u/k*(x-x0)Thus(a*y^2/2 - y^3/3) - (a*y0^2/2 - y0^3/3) = u/k*(x-x0)and the inverse function if the solution is given byx = x0 + k/u*((a*y^2/2 - y^3/3) - (a*y0^2/2 - y0^3/3))Best wishesTorsten. Related SolutionsMATLAB: Problem solving a system of differential equations uspan=0:0.1:1;K=3;g=0.1;dydu=@(u,y)[(-2*u*y(1)-K*(y(1)*u-(1+g)))/(1+u^2+K*u*(u-(1+g)/y(1))) (1-u^2)/(1+u^2+K*u*(u-(1+g)/y(1))) (2*u+K*u^2*(u-(1+g)/y(1)))/(1+u^2+K*u*(u-(1+g)/y(1)))];[U,Y]=ode45(dydu,uspan,[1 0 0]);plot(U,Y(:,1),U,Y(:,2),U,Y(:,3));Best wishesTorsten. MATLAB: 2nd order numerical differential equation system solving function mainy0=[0; 5; 1; 1; 1; 4; 1; 1; 2; 3; 1; 1];t0=0;tfinal=10;[T Y] = ode45(@odesNew,[t0 tfinal],y0)function dy = odesNew(t,y)G=6.673*10^-11;m1=1; m2=2; m3=3;dy=zeros(12,1);x1=y(1);x2=y(2);x3=y(3);y1=y(4);y2=y(5);y3=y(6);u1=y(7);u2=y(8);u3=y(9);v1=y(10);v2=y(11);v3=y(12);%Körper 1/Mass1dy(1)=u1;dy(4)=v1;dy(7)=(((G*m1*m2)/((x2-x1)^2+(y2-y1)^2)^(3/2))*(x2-x1)+((G*m1*m3)/((x3-x1)^2+(y3-y1)^2)^(3/2))*(x3-x1))/m1;dy(10)=(((G*m1*m2)/((x2-x1)^2+(y2-y1)^2)^(3/2))*(y2-y1)+((G*m1*m3)/((x3-x1)^2+(y3-y1)^2)^(3/2))*(y3-y1))/m1;%Körper 2/Mass2dy(2)=u2;dy(5)=v2;dy(8)=(((G*m2*m3)/((x3-x2)^2+(y3-y2)^2)^(3/2))*(x3-x2)+((G*m1*m2)/((x1-x2)^2+(y1-y2)^2)^(3/2))*(x1-x2))/m2;dy(11)=(((G*m2*m3)/((x3-x2)^2+(y3-y2)^2)^(3/2))*(y3-y2)+((G*m1*m2)/((x1-x2)^2+(y1-y2)^2)^(3/2))*(y1-y2))/m2;%Körper 3/Mass3dy(3)=u3;dy(6)=v3;dy(9)=(((G*m3*m1)/((x1-x3)^2+(y1-y3)^2)^(3/2))*(x1-x3)+((G*m3*m2)/((x2-x3)^2+(y2-y3)^2)^(3/2))*(x2-x3))/m3;dy(12)=(((G*m3*m1)/((x1-x3)^2+(y1-y3)^2)^(3/2))*(y1-y3)+((G*m3*m2)/((x2-x3)^2+(y2-y3)^2)^(3/2))*(y2-y3))/m3;Best wishesTorsten. Related QuestionUse of ode45 for projectile trajectory including dragPlotting bacterial growth curve with ODEs – ‘too many input arguments’ error
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