Internal problem ID [3909]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 23
Problem number: 662.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{2} y^{\prime } x^{2}=-x^{3}+x -1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 155
dsolve(x^2*y(x)^2*diff(y(x),x)+1-x+x^3 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {{\left (\left (-12 x^{3}+24 x \ln \left (x \right )+8 c_{1} x +24\right ) x^{2}\right )}^{\frac {1}{3}}}{2 x} y \left (x \right ) = -\frac {{\left (\left (-12 x^{3}+24 x \ln \left (x \right )+8 c_{1} x +24\right ) x^{2}\right )}^{\frac {1}{3}}}{4 x}-\frac {i \sqrt {3}\, {\left (\left (-12 x^{3}+24 x \ln \left (x \right )+8 c_{1} x +24\right ) x^{2}\right )}^{\frac {1}{3}}}{4 x} y \left (x \right ) = -\frac {{\left (\left (-12 x^{3}+24 x \ln \left (x \right )+8 c_{1} x +24\right ) x^{2}\right )}^{\frac {1}{3}}}{4 x}+\frac {i \sqrt {3}\, {\left (\left (-12 x^{3}+24 x \ln \left (x \right )+8 c_{1} x +24\right ) x^{2}\right )}^{\frac {1}{3}}}{4 x} \end{align*}
✓ Solution by Mathematica
Time used: 0.341 (sec). Leaf size: 111
DSolve[x^2 y[x]^2 y'[x]+1-x+x^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt [3]{-\frac {3}{2}} \sqrt [3]{-x^3+2 x \log (x)+2 c_1 x+2}}{\sqrt [3]{x}} y(x)\to \frac {\sqrt [3]{-\frac {3 x^3}{2}+3 x \log (x)+3 c_1 x+3}}{\sqrt [3]{x}} y(x)\to \frac {(-1)^{2/3} \sqrt [3]{-\frac {3 x^3}{2}+3 x \log (x)+3 c_1 x+3}}{\sqrt [3]{x}} \end{align*}