Internal problem ID [5319]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 6. Equations of first order and first degree (Linear equations). Supplemetary
problems. Page 39
Problem number: 23 (b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
\[ \boxed {4 y x^{2} y^{\prime }-3 x \left (3 y^{2}+2\right )-2 \left (3 y^{2}+2\right )^{3}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 175
dsolve(4*x^2*y(x)*diff(y(x),x)=3*x*(3*y(x)^2+2)+2*(3*y(x)^2+2)^3,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {\sqrt {6}\, \sqrt {\frac {-3 c_{1} x^{8}+\sqrt {-3 \left (c_{1} x^{8}-\frac {1}{3}\right ) c_{1} x^{9}}+1}{3 c_{1} x^{8}-1}}}{3} \\ y \left (x \right ) &= \frac {\sqrt {6}\, \sqrt {\frac {-3 c_{1} x^{8}+\sqrt {-3 \left (c_{1} x^{8}-\frac {1}{3}\right ) c_{1} x^{9}}+1}{3 c_{1} x^{8}-1}}}{3} \\ y \left (x \right ) &= -\frac {\sqrt {\frac {-18 c_{1} x^{8}-6 \sqrt {-3 \left (c_{1} x^{8}-\frac {1}{3}\right ) c_{1} x^{9}}+6}{3 c_{1} x^{8}-1}}}{3} \\ y \left (x \right ) &= \frac {\sqrt {\frac {-18 c_{1} x^{8}-6 \sqrt {-3 \left (c_{1} x^{8}-\frac {1}{3}\right ) c_{1} x^{9}}+6}{3 c_{1} x^{8}-1}}}{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 19.518 (sec). Leaf size: 277
DSolve[4*x^2*y[x]*y'[x]==3*x*(3*y[x]^2+2)+2*(3*y[x]^2+2)^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{3} \sqrt {2} \sqrt {-\frac {3 x^8+\sqrt {3} \sqrt {-x^9 \left (x^8+72 c_1\right )}+216 c_1}{x^8+72 c_1}} \\ y(x)\to \frac {1}{3} \sqrt {2} \sqrt {-\frac {3 x^8+\sqrt {3} \sqrt {-x^9 \left (x^8+72 c_1\right )}+216 c_1}{x^8+72 c_1}} \\ y(x)\to -\frac {1}{3} \sqrt {2} \sqrt {\frac {-3 x^8+\sqrt {3} \sqrt {-x^9 \left (x^8+72 c_1\right )}-216 c_1}{x^8+72 c_1}} \\ y(x)\to \frac {1}{3} \sqrt {2} \sqrt {\frac {-3 x^8+\sqrt {3} \sqrt {-x^9 \left (x^8+72 c_1\right )}-216 c_1}{x^8+72 c_1}} \\ y(x)\to -i \sqrt {\frac {2}{3}} \\ y(x)\to i \sqrt {\frac {2}{3}} \\ \end{align*}