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Exact solution of ode using matlab dy/dx=x^2+y^2 condition y(0)=0

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clear all clc close all syms y(x) ode=(diff(y,x)+((y))==(x^2)+(y^2) cond = y(0) ==1; ySol(x)=dsolve(ode,cond) ySol(x)= -x^2-2*x-2+2*exp(x)

Accepted Answer

Bjorn Gustavsson
Bjorn Gustavsson on 28 Jun 2021
That is a Riccatti ODE. See Riccati_equation for information on how to solve it analytically. My version of matlab spits out a longish answer.

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