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first order differential equation

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ikhlas
ikhlas 2022-12-17
回答： Star Strider 2022-12-17
how can we solve this differential equation numerically in matlab
2xy(dy/dx)+(1+x)y^2=e^x ?

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Star Strider
Star Strider 2022-12-17
Ran in:
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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