Internal problem ID [4588]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 24. First order differential equations. Further problems 24. page 1068
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {\left (x^{3}+3 y^{2} x \right ) y^{\prime }-y^{3}-3 x^{2} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 23
dsolve((x^3+3*x*y(x)^2)*diff(y(x),x)=y(x)^3+3*x^2*y(x),y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (\textit {\_Z}^{4} x c_{1}-c_{1} x -\textit {\_Z} \right )^{2} x \]
✓ Solution by Mathematica
Time used: 60.26 (sec). Leaf size: 1659
DSolve[(x^3+3*x*y[x]^2)*y'[x]==y[x]^3+3*x^2*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} \left (-\sqrt {3} \sqrt {4 x^2+\frac {16 \sqrt [3]{2} x^4}{\sqrt [3]{128 x^6+27 e^{2 c_1} x^2+3 \sqrt {768 e^{2 c_1} x^8+81 e^{4 c_1} x^4}}}+\frac {\sqrt [3]{128 x^6+27 e^{2 c_1} x^2+3 \sqrt {768 e^{2 c_1} x^8+81 e^{4 c_1} x^4}}}{\sqrt [3]{2}}}-3 \sqrt {\frac {8 x^2}{3}-\frac {16 \sqrt [3]{2} x^4}{3 \sqrt [3]{128 x^6+27 e^{2 c_1} x^2+3 \sqrt {768 e^{2 c_1} x^8+81 e^{4 c_1} x^4}}}-\frac {2 \sqrt {3} e^{c_1} x}{\sqrt {4 x^2+\frac {16 \sqrt [3]{2} x^4}{\sqrt [3]{128 x^6+27 e^{2 c_1} x^2+3 \sqrt {768 e^{2 c_1} x^8+81 e^{4 c_1} x^4}}}+\frac {\sqrt [3]{128 x^6+27 e^{2 c_1} x^2+3 \sqrt {768 e^{2 c_1} x^8+81 e^{4 c_1} x^4}}}{\sqrt [3]{2}}}}-\frac {\sqrt [3]{128 x^6+27 e^{2 c_1} x^2+3 \sqrt {768 e^{2 c_1} x^8+81 e^{4 c_1} x^4}}}{3 \sqrt [3]{2}}}\right ) \\ y(x)\to \frac {1}{6} \left (3 \sqrt {\frac {8 x^2}{3}-\frac {16 \sqrt [3]{2} x^4}{3 \sqrt [3]{128 x^6+27 e^{2 c_1} x^2+3 \sqrt {768 e^{2 c_1} x^8+81 e^{4 c_1} x^4}}}-\frac {2 \sqrt {3} e^{c_1} x}{\sqrt {4 x^2+\frac {16 \sqrt [3]{2} x^4}{\sqrt [3]{128 x^6+27 e^{2 c_1} x^2+3 \sqrt {768 e^{2 c_1} x^8+81 e^{4 c_1} x^4}}}+\frac {\sqrt [3]{128 x^6+27 e^{2 c_1} x^2+3 \sqrt {768 e^{2 c_1} x^8+81 e^{4 c_1} x^4}}}{\sqrt [3]{2}}}}-\frac {\sqrt [3]{128 x^6+27 e^{2 c_1} x^2+3 \sqrt {768 e^{2 c_1} x^8+81 e^{4 c_1} x^4}}}{3 \sqrt [3]{2}}}-\sqrt {3} \sqrt {4 x^2+\frac {16 \sqrt [3]{2} x^4}{\sqrt [3]{128 x^6+27 e^{2 c_1} x^2+3 \sqrt {768 e^{2 c_1} x^8+81 e^{4 c_1} x^4}}}+\frac {\sqrt [3]{128 x^6+27 e^{2 c_1} x^2+3 \sqrt {768 e^{2 c_1} x^8+81 e^{4 c_1} x^4}}}{\sqrt [3]{2}}}\right ) \\ y(x)\to \frac {1}{6} \left (\sqrt {3} \sqrt {4 x^2+\frac {16 \sqrt [3]{2} x^4}{\sqrt [3]{128 x^6+27 e^{2 c_1} x^2+3 \sqrt {768 e^{2 c_1} x^8+81 e^{4 c_1} x^4}}}+\frac {\sqrt [3]{128 x^6+27 e^{2 c_1} x^2+3 \sqrt {768 e^{2 c_1} x^8+81 e^{4 c_1} x^4}}}{\sqrt [3]{2}}}-3 \sqrt {\frac {8 x^2}{3}-\frac {16 \sqrt [3]{2} x^4}{3 \sqrt [3]{128 x^6+27 e^{2 c_1} x^2+3 \sqrt {768 e^{2 c_1} x^8+81 e^{4 c_1} x^4}}}+\frac {2 \sqrt {3} e^{c_1} x}{\sqrt {4 x^2+\frac {16 \sqrt [3]{2} x^4}{\sqrt [3]{128 x^6+27 e^{2 c_1} x^2+3 \sqrt {768 e^{2 c_1} x^8+81 e^{4 c_1} x^4}}}+\frac {\sqrt [3]{128 x^6+27 e^{2 c_1} x^2+3 \sqrt {768 e^{2 c_1} x^8+81 e^{4 c_1} x^4}}}{\sqrt [3]{2}}}}-\frac {\sqrt [3]{128 x^6+27 e^{2 c_1} x^2+3 \sqrt {768 e^{2 c_1} x^8+81 e^{4 c_1} x^4}}}{3 \sqrt [3]{2}}}\right ) \\ y(x)\to \frac {1}{6} \left (\sqrt {3} \sqrt {4 x^2+\frac {16 \sqrt [3]{2} x^4}{\sqrt [3]{128 x^6+27 e^{2 c_1} x^2+3 \sqrt {768 e^{2 c_1} x^8+81 e^{4 c_1} x^4}}}+\frac {\sqrt [3]{128 x^6+27 e^{2 c_1} x^2+3 \sqrt {768 e^{2 c_1} x^8+81 e^{4 c_1} x^4}}}{\sqrt [3]{2}}}+3 \sqrt {\frac {8 x^2}{3}-\frac {16 \sqrt [3]{2} x^4}{3 \sqrt [3]{128 x^6+27 e^{2 c_1} x^2+3 \sqrt {768 e^{2 c_1} x^8+81 e^{4 c_1} x^4}}}+\frac {2 \sqrt {3} e^{c_1} x}{\sqrt {4 x^2+\frac {16 \sqrt [3]{2} x^4}{\sqrt [3]{128 x^6+27 e^{2 c_1} x^2+3 \sqrt {768 e^{2 c_1} x^8+81 e^{4 c_1} x^4}}}+\frac {\sqrt [3]{128 x^6+27 e^{2 c_1} x^2+3 \sqrt {768 e^{2 c_1} x^8+81 e^{4 c_1} x^4}}}{\sqrt [3]{2}}}}-\frac {\sqrt [3]{128 x^6+27 e^{2 c_1} x^2+3 \sqrt {768 e^{2 c_1} x^8+81 e^{4 c_1} x^4}}}{3 \sqrt [3]{2}}}\right ) \\ \end{align*}