Internal problem ID [3825]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 20
Problem number: 575.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _rational, _Bernoulli]
\[ \boxed {2 x^{2} y y^{\prime }+y^{2}=x^{2} \left (1+2 x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve(2*x^2*y(x)*diff(y(x),x) = x^2*(1+2*x)-y(x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \sqrt {{\mathrm e}^{\frac {1}{x}} c_{1} +x^{2}} y \left (x \right ) = -\sqrt {{\mathrm e}^{\frac {1}{x}} c_{1} +x^{2}} \end{align*}
✓ Solution by Mathematica
Time used: 7.192 (sec). Leaf size: 43
DSolve[2 x^2 y[x] y'[x]==x^2(1+2 x)-y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x^2+c_1 e^{\frac {1}{x}}} y(x)\to \sqrt {x^2+c_1 e^{\frac {1}{x}}} \end{align*}