Internal problem ID [3401]
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]
Solve \begin {gather*} \boxed {x^{2} y^{2} y^{\prime }+1-x +x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (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 \relax (x ) = \frac {\left (\left (-12 x^{3}+24 \ln \relax (x ) x +8 c_{1} x +24\right ) x^{2}\right )^{\frac {1}{3}}}{2 x} \\ y \relax (x ) = -\frac {\left (\left (-12 x^{3}+24 \ln \relax (x ) x +8 c_{1} x +24\right ) x^{2}\right )^{\frac {1}{3}}}{4 x}-\frac {i \sqrt {3}\, \left (\left (-12 x^{3}+24 \ln \relax (x ) x +8 c_{1} x +24\right ) x^{2}\right )^{\frac {1}{3}}}{4 x} \\ y \relax (x ) = -\frac {\left (\left (-12 x^{3}+24 \ln \relax (x ) x +8 c_{1} x +24\right ) x^{2}\right )^{\frac {1}{3}}}{4 x}+\frac {i \sqrt {3}\, \left (\left (-12 x^{3}+24 \ln \relax (x ) x +8 c_{1} x +24\right ) x^{2}\right )^{\frac {1}{3}}}{4 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.265 (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*}