80.5.2 problem 3
Internal
problem
ID
[18560]
Book
:
Elementary
Differential
Equations.
By
Thornton
C.
Fry.
D
Van
Nostrand.
NY.
First
Edition
(1929)
Section
:
Chapter
IV.
Methods
of
solution:
First
order
equations.
section
32.
Problems
at
page
89
Problem
number
:
3
Date
solved
:
Tuesday, January 28, 2025 at 11:58:59 AM
CAS
classification
:
[_quadrature]
\begin{align*} 2 {y^{\prime }}^{3}+{y^{\prime }}^{2}-y&=0 \end{align*}
✓ Solution by Maple
Time used: 0.019 (sec). Leaf size: 385
dsolve(2*diff(y(x),x)^3+diff(y(x),x)^2-y(x)=0,y(x), singsol=all)
\begin{align*}
y \left (x \right ) &= 0 \\
-6 \sqrt {3}\, \left (\int _{}^{y \left (x \right )}\frac {\left (18 \sqrt {27 \textit {\_a}^{2}-\textit {\_a}}+\left (54 \textit {\_a} -1\right ) \sqrt {3}\right )^{{1}/{3}}}{3^{{2}/{3}}-\sqrt {3}\, \left (18 \sqrt {27 \textit {\_a}^{2}-\textit {\_a}}+\left (54 \textit {\_a} -1\right ) \sqrt {3}\right )^{{1}/{3}}+3^{{1}/{3}} \left (18 \sqrt {27 \textit {\_a}^{2}-\textit {\_a}}+\left (54 \textit {\_a} -1\right ) \sqrt {3}\right )^{{2}/{3}}}d \textit {\_a} \right )+x -c_{1} &= 0 \\
\frac {-72 \left (\int _{}^{y \left (x \right )}\frac {\left (18 \sqrt {27 \textit {\_a}^{2}-\textit {\_a}}+\left (54 \textit {\_a} -1\right ) \sqrt {3}\right )^{{1}/{3}}}{\left (i 3^{{5}/{6}}+3^{{1}/{3}}-2 \,3^{{1}/{6}} \left (18 \sqrt {27 \textit {\_a}^{2}-\textit {\_a}}+\left (54 \textit {\_a} -1\right ) \sqrt {3}\right )^{{1}/{3}}\right ) \left (3^{{1}/{3}}+3^{{1}/{6}} \left (18 \sqrt {27 \textit {\_a}^{2}-\textit {\_a}}+\left (54 \textit {\_a} -1\right ) \sqrt {3}\right )^{{1}/{3}}\right )}d \textit {\_a} \right )+\left (-c_{1} +x \right ) \sqrt {3}+3 i x -3 i c_{1}}{\sqrt {3}+3 i} &= 0 \\
\frac {72 \left (\int _{}^{y \left (x \right )}\frac {\left (18 \sqrt {27 \textit {\_a}^{2}-\textit {\_a}}+\left (54 \textit {\_a} -1\right ) \sqrt {3}\right )^{{1}/{3}}}{\left (-i 3^{{5}/{6}}+3^{{1}/{3}}-2 \,3^{{1}/{6}} \left (18 \sqrt {27 \textit {\_a}^{2}-\textit {\_a}}+\left (54 \textit {\_a} -1\right ) \sqrt {3}\right )^{{1}/{3}}\right ) \left (3^{{1}/{3}}+3^{{1}/{6}} \left (18 \sqrt {27 \textit {\_a}^{2}-\textit {\_a}}+\left (54 \textit {\_a} -1\right ) \sqrt {3}\right )^{{1}/{3}}\right )}d \textit {\_a} \right )+\left (-x +c_{1} \right ) \sqrt {3}+3 i x -3 i c_{1}}{-\sqrt {3}+3 i} &= 0 \\
\end{align*}
✗ Solution by Mathematica
Time used: 0.000 (sec). Leaf size: 0
DSolve[2*D[y[x],x]^3+D[y[x],x]^2-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Timed out