Internal problem ID [12472]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 74.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _exact, _rational]
\[ \boxed {\left (y^{3}-x \right ) y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve((y(x)^3-x)*diff(y(x),x)=y(x),y(x), singsol=all)
\[ -\frac {c_{1}}{y \left (x \right )}+x -\frac {y \left (x \right )^{3}}{4} = 0 \]
✓ Solution by Mathematica
Time used: 57.499 (sec). Leaf size: 996
DSolve[(y[x]^3-x)*y'[x]==y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {\frac {\left (9 x^2-\sqrt {81 x^4-192 c_1{}^3}\right ){}^{2/3}+4 \sqrt [3]{3} c_1}{\sqrt [3]{9 x^2-\sqrt {81 x^4-192 c_1{}^3}}}}}{\sqrt {2} \sqrt [3]{3}}-\frac {1}{2} \sqrt {-\frac {4 \sqrt {2} \sqrt [3]{3} x}{\sqrt {\frac {\left (9 x^2-\sqrt {81 x^4-192 c_1{}^3}\right ){}^{2/3}+4 \sqrt [3]{3} c_1}{\sqrt [3]{9 x^2-\sqrt {81 x^4-192 c_1{}^3}}}}}-\frac {2 \sqrt [3]{9 x^2-\sqrt {81 x^4-192 c_1{}^3}}}{3^{2/3}}-\frac {8 c_1}{\sqrt [3]{27 x^2-3 \sqrt {81 x^4-192 c_1{}^3}}}} \\ y(x)\to \frac {1}{2} \left (\sqrt {-\frac {4 \sqrt {2} \sqrt [3]{3} x}{\sqrt {\frac {\left (9 x^2-\sqrt {81 x^4-192 c_1{}^3}\right ){}^{2/3}+4 \sqrt [3]{3} c_1}{\sqrt [3]{9 x^2-\sqrt {81 x^4-192 c_1{}^3}}}}}-\frac {2 \sqrt [3]{9 x^2-\sqrt {81 x^4-192 c_1{}^3}}}{3^{2/3}}-\frac {8 c_1}{\sqrt [3]{27 x^2-3 \sqrt {81 x^4-192 c_1{}^3}}}}-\frac {\sqrt {2} \sqrt {\frac {\left (9 x^2-\sqrt {81 x^4-192 c_1{}^3}\right ){}^{2/3}+4 \sqrt [3]{3} c_1}{\sqrt [3]{9 x^2-\sqrt {81 x^4-192 c_1{}^3}}}}}{\sqrt [3]{3}}\right ) \\ y(x)\to \frac {\sqrt {\frac {\left (9 x^2-\sqrt {81 x^4-192 c_1{}^3}\right ){}^{2/3}+4 \sqrt [3]{3} c_1}{\sqrt [3]{9 x^2-\sqrt {81 x^4-192 c_1{}^3}}}}}{\sqrt {2} \sqrt [3]{3}}-\frac {1}{2} \sqrt {\frac {4 \sqrt {2} \sqrt [3]{3} x}{\sqrt {\frac {\left (9 x^2-\sqrt {81 x^4-192 c_1{}^3}\right ){}^{2/3}+4 \sqrt [3]{3} c_1}{\sqrt [3]{9 x^2-\sqrt {81 x^4-192 c_1{}^3}}}}}-\frac {2 \sqrt [3]{9 x^2-\sqrt {81 x^4-192 c_1{}^3}}}{3^{2/3}}-\frac {8 c_1}{\sqrt [3]{27 x^2-3 \sqrt {81 x^4-192 c_1{}^3}}}} \\ y(x)\to \frac {1}{2} \left (\frac {\sqrt {2} \sqrt {\frac {\left (9 x^2-\sqrt {81 x^4-192 c_1{}^3}\right ){}^{2/3}+4 \sqrt [3]{3} c_1}{\sqrt [3]{9 x^2-\sqrt {81 x^4-192 c_1{}^3}}}}}{\sqrt [3]{3}}+\sqrt {\frac {4 \sqrt {2} \sqrt [3]{3} x}{\sqrt {\frac {\left (9 x^2-\sqrt {81 x^4-192 c_1{}^3}\right ){}^{2/3}+4 \sqrt [3]{3} c_1}{\sqrt [3]{9 x^2-\sqrt {81 x^4-192 c_1{}^3}}}}}-\frac {2 \sqrt [3]{9 x^2-\sqrt {81 x^4-192 c_1{}^3}}}{3^{2/3}}-\frac {8 c_1}{\sqrt [3]{27 x^2-3 \sqrt {81 x^4-192 c_1{}^3}}}}\right ) \\ y(x)\to 0 \\ \end{align*}