Internal problem ID [13415]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 7. The exact form and general integrating fators. Additional exercises. page
141
Problem number: 7.5 (b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {y+\left (y^{4}-3 x \right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(y(x)+(y(x)^4-3*x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right )^{4}-y \left (x \right )^{3} c_{1} +x = 0 \]
✓ Solution by Mathematica
Time used: 43.447 (sec). Leaf size: 1270
DSolve[y[x]+(y[x]^4-3*x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} \sqrt {\frac {\sqrt [3]{\sqrt {-768 x^3+81 c_1{}^4 x^2}+9 c_1{}^2 x}}{\sqrt [3]{2} 3^{2/3}}+\frac {4 \sqrt [3]{\frac {2}{3}} x}{\sqrt [3]{\sqrt {-768 x^3+81 c_1{}^4 x^2}+9 c_1{}^2 x}}+\frac {c_1{}^2}{4}}-\frac {1}{2} \sqrt {-\frac {c_1{}^3}{4 \sqrt {\frac {\sqrt [3]{\sqrt {-768 x^3+81 c_1{}^4 x^2}+9 c_1{}^2 x}}{\sqrt [3]{2} 3^{2/3}}+\frac {4 \sqrt [3]{\frac {2}{3}} x}{\sqrt [3]{\sqrt {-768 x^3+81 c_1{}^4 x^2}+9 c_1{}^2 x}}+\frac {c_1{}^2}{4}}}-\frac {\sqrt [3]{\sqrt {-768 x^3+81 c_1{}^4 x^2}+9 c_1{}^2 x}}{\sqrt [3]{2} 3^{2/3}}-\frac {4 \sqrt [3]{\frac {2}{3}} x}{\sqrt [3]{\sqrt {-768 x^3+81 c_1{}^4 x^2}+9 c_1{}^2 x}}+\frac {c_1{}^2}{2}}+\frac {c_1}{4} \\ y(x)\to -\frac {1}{2} \sqrt {\frac {\sqrt [3]{\sqrt {-768 x^3+81 c_1{}^4 x^2}+9 c_1{}^2 x}}{\sqrt [3]{2} 3^{2/3}}+\frac {4 \sqrt [3]{\frac {2}{3}} x}{\sqrt [3]{\sqrt {-768 x^3+81 c_1{}^4 x^2}+9 c_1{}^2 x}}+\frac {c_1{}^2}{4}}+\frac {1}{2} \sqrt {-\frac {c_1{}^3}{4 \sqrt {\frac {\sqrt [3]{\sqrt {-768 x^3+81 c_1{}^4 x^2}+9 c_1{}^2 x}}{\sqrt [3]{2} 3^{2/3}}+\frac {4 \sqrt [3]{\frac {2}{3}} x}{\sqrt [3]{\sqrt {-768 x^3+81 c_1{}^4 x^2}+9 c_1{}^2 x}}+\frac {c_1{}^2}{4}}}-\frac {\sqrt [3]{\sqrt {-768 x^3+81 c_1{}^4 x^2}+9 c_1{}^2 x}}{\sqrt [3]{2} 3^{2/3}}-\frac {4 \sqrt [3]{\frac {2}{3}} x}{\sqrt [3]{\sqrt {-768 x^3+81 c_1{}^4 x^2}+9 c_1{}^2 x}}+\frac {c_1{}^2}{2}}+\frac {c_1}{4} \\ y(x)\to \frac {1}{2} \sqrt {\frac {\sqrt [3]{\sqrt {-768 x^3+81 c_1{}^4 x^2}+9 c_1{}^2 x}}{\sqrt [3]{2} 3^{2/3}}+\frac {4 \sqrt [3]{\frac {2}{3}} x}{\sqrt [3]{\sqrt {-768 x^3+81 c_1{}^4 x^2}+9 c_1{}^2 x}}+\frac {c_1{}^2}{4}}-\frac {1}{2} \sqrt {\frac {c_1{}^3}{4 \sqrt {\frac {\sqrt [3]{\sqrt {-768 x^3+81 c_1{}^4 x^2}+9 c_1{}^2 x}}{\sqrt [3]{2} 3^{2/3}}+\frac {4 \sqrt [3]{\frac {2}{3}} x}{\sqrt [3]{\sqrt {-768 x^3+81 c_1{}^4 x^2}+9 c_1{}^2 x}}+\frac {c_1{}^2}{4}}}-\frac {\sqrt [3]{\sqrt {-768 x^3+81 c_1{}^4 x^2}+9 c_1{}^2 x}}{\sqrt [3]{2} 3^{2/3}}-\frac {4 \sqrt [3]{\frac {2}{3}} x}{\sqrt [3]{\sqrt {-768 x^3+81 c_1{}^4 x^2}+9 c_1{}^2 x}}+\frac {c_1{}^2}{2}}+\frac {c_1}{4} \\ y(x)\to \frac {1}{2} \sqrt {\frac {\sqrt [3]{\sqrt {-768 x^3+81 c_1{}^4 x^2}+9 c_1{}^2 x}}{\sqrt [3]{2} 3^{2/3}}+\frac {4 \sqrt [3]{\frac {2}{3}} x}{\sqrt [3]{\sqrt {-768 x^3+81 c_1{}^4 x^2}+9 c_1{}^2 x}}+\frac {c_1{}^2}{4}}+\frac {1}{2} \sqrt {\frac {c_1{}^3}{4 \sqrt {\frac {\sqrt [3]{\sqrt {-768 x^3+81 c_1{}^4 x^2}+9 c_1{}^2 x}}{\sqrt [3]{2} 3^{2/3}}+\frac {4 \sqrt [3]{\frac {2}{3}} x}{\sqrt [3]{\sqrt {-768 x^3+81 c_1{}^4 x^2}+9 c_1{}^2 x}}+\frac {c_1{}^2}{4}}}-\frac {\sqrt [3]{\sqrt {-768 x^3+81 c_1{}^4 x^2}+9 c_1{}^2 x}}{\sqrt [3]{2} 3^{2/3}}-\frac {4 \sqrt [3]{\frac {2}{3}} x}{\sqrt [3]{\sqrt {-768 x^3+81 c_1{}^4 x^2}+9 c_1{}^2 x}}+\frac {c_1{}^2}{2}}+\frac {c_1}{4} \\ y(x)\to 0 \\ \end{align*}