first order differential equation

how can we solve this differential equation numerically in matlab

2xy(dy/dx)+(1+x)y^2=e^x ?

Answer 1

[Star Strider]

One approach —

syms y(x) x Y 
Dy = diff(y);
Eqn = 2*x*y*Dy+(1+x)*y^2 == exp(x);
[VF,Subs] = odeToVectorField(Eqn)

VF = 

Subs = 

odefcn = matlabFunction(VF, 'Vars',{x,Y})

odefcn = function_handle with value:
    @(x,Y)[((-exp(x)+Y(1).^2+x.*Y(1).^2).*(-1.0./2.0))./(x.*Y(1))]

Then, use ‘odefcn’ in the differential equation solver (perhaps ode45) of your choice.

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