Internal problem ID [3091]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, section 8, page 41
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational]
\[ \boxed {y+\left (x +y^{3}\right ) y^{\prime }=x^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve((y(x)-x^3)+(x+y(x)^3)*diff(y(x),x)=0,y(x), singsol=all)
\[ -\frac {x^{4}}{4}+y \left (x \right ) x +\frac {y \left (x \right )^{4}}{4}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 60.173 (sec). Leaf size: 1210
DSolve[(y[x]-x^3)+(x+y[x]^3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {\sqrt [3]{9 x^2+\sqrt {3} \sqrt {27 x^4+\left (x^4+4 c_1\right ){}^3}}-\frac {\sqrt [3]{3} \left (x^4+4 c_1\right )}{\sqrt [3]{9 x^2+\sqrt {3} \sqrt {27 x^4+\left (x^4+4 c_1\right ){}^3}}}}+\sqrt {\frac {6 \sqrt {2} x}{\sqrt {\sqrt [3]{9 x^2+\sqrt {3} \sqrt {27 x^4+\left (x^4+4 c_1\right ){}^3}}-\frac {\sqrt [3]{3} \left (x^4+4 c_1\right )}{\sqrt [3]{9 x^2+\sqrt {3} \sqrt {27 x^4+\left (x^4+4 c_1\right ){}^3}}}}}-\sqrt [3]{9 x^2+\sqrt {3} \sqrt {27 x^4+\left (x^4+4 c_1\right ){}^3}}+\frac {\sqrt [3]{3} \left (x^4+4 c_1\right )}{\sqrt [3]{9 x^2+\sqrt {3} \sqrt {27 x^4+\left (x^4+4 c_1\right ){}^3}}}}}{\sqrt {2} \sqrt [3]{3}} y(x)\to \frac {\sqrt {\frac {6 \sqrt {2} x}{\sqrt {\sqrt [3]{9 x^2+\sqrt {3} \sqrt {27 x^4+\left (x^4+4 c_1\right ){}^3}}-\frac {\sqrt [3]{3} \left (x^4+4 c_1\right )}{\sqrt [3]{9 x^2+\sqrt {3} \sqrt {27 x^4+\left (x^4+4 c_1\right ){}^3}}}}}-\sqrt [3]{9 x^2+\sqrt {3} \sqrt {27 x^4+\left (x^4+4 c_1\right ){}^3}}+\frac {\sqrt [3]{3} \left (x^4+4 c_1\right )}{\sqrt [3]{9 x^2+\sqrt {3} \sqrt {27 x^4+\left (x^4+4 c_1\right ){}^3}}}}-\sqrt {\sqrt [3]{9 x^2+\sqrt {3} \sqrt {27 x^4+\left (x^4+4 c_1\right ){}^3}}-\frac {\sqrt [3]{3} \left (x^4+4 c_1\right )}{\sqrt [3]{9 x^2+\sqrt {3} \sqrt {27 x^4+\left (x^4+4 c_1\right ){}^3}}}}}{\sqrt {2} \sqrt [3]{3}} y(x)\to \frac {\sqrt {\sqrt [3]{9 x^2+\sqrt {3} \sqrt {27 x^4+\left (x^4+4 c_1\right ){}^3}}-\frac {\sqrt [3]{3} \left (x^4+4 c_1\right )}{\sqrt [3]{9 x^2+\sqrt {3} \sqrt {27 x^4+\left (x^4+4 c_1\right ){}^3}}}}-\sqrt {-\frac {6 \sqrt {2} x}{\sqrt {\sqrt [3]{9 x^2+\sqrt {3} \sqrt {27 x^4+\left (x^4+4 c_1\right ){}^3}}-\frac {\sqrt [3]{3} \left (x^4+4 c_1\right )}{\sqrt [3]{9 x^2+\sqrt {3} \sqrt {27 x^4+\left (x^4+4 c_1\right ){}^3}}}}}-\sqrt [3]{9 x^2+\sqrt {3} \sqrt {27 x^4+\left (x^4+4 c_1\right ){}^3}}+\frac {\sqrt [3]{3} \left (x^4+4 c_1\right )}{\sqrt [3]{9 x^2+\sqrt {3} \sqrt {27 x^4+\left (x^4+4 c_1\right ){}^3}}}}}{\sqrt {2} \sqrt [3]{3}} y(x)\to \frac {\sqrt {\sqrt [3]{9 x^2+\sqrt {3} \sqrt {27 x^4+\left (x^4+4 c_1\right ){}^3}}-\frac {\sqrt [3]{3} \left (x^4+4 c_1\right )}{\sqrt [3]{9 x^2+\sqrt {3} \sqrt {27 x^4+\left (x^4+4 c_1\right ){}^3}}}}+\sqrt {-\frac {6 \sqrt {2} x}{\sqrt {\sqrt [3]{9 x^2+\sqrt {3} \sqrt {27 x^4+\left (x^4+4 c_1\right ){}^3}}-\frac {\sqrt [3]{3} \left (x^4+4 c_1\right )}{\sqrt [3]{9 x^2+\sqrt {3} \sqrt {27 x^4+\left (x^4+4 c_1\right ){}^3}}}}}-\sqrt [3]{9 x^2+\sqrt {3} \sqrt {27 x^4+\left (x^4+4 c_1\right ){}^3}}+\frac {\sqrt [3]{3} \left (x^4+4 c_1\right )}{\sqrt [3]{9 x^2+\sqrt {3} \sqrt {27 x^4+\left (x^4+4 c_1\right ){}^3}}}}}{\sqrt {2} \sqrt [3]{3}} \end{align*}