What is the solution for xe^{x^2}+yy^'=0,y(0)=1 ?

The solution for xe^{x^2}+yy^'=0,y(0)=1 is y=sqrt(-e^{x^2)+2}

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xe^{x^2}+yy^'=0,y(0)=1

x e^{x^{2}} + y y^{^{'}} = 0, y (0) = 1

y = - e^{x^{2}} + 2

Solution steps

x e^{x^{2}} + y y^{'} (x) = 0

Solve separable ODE:

y = - e^{x^{2}} + 2

y = - e^{x^{2}} + 2

\frac{d y}{d x} = - \frac{0.8}{cos ( y )}, y (0) = \frac{π}{4}

\frac{1}{1 - 2 y} d y = x d x

\frac{d x}{y ^{2}} = \frac{d y}{x ^{2}}

x^{^{'}} = - \frac{15 x}{1000}, x (0) = 15

e^{x^{3} - y^{2}} + \frac{y}{x ^{2}} y^{^{'}} = 0

What is the solution for xe^{x^2}+yy^'=0,y(0)=1 ?
The solution for xe^{x^2}+yy^'=0,y(0)=1 is y=sqrt(-e^{x^2)+2}