60.7.4 problem 1594 (6.4)
Internal
problem
ID
[11593]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
6,
non-linear
second
order
Problem
number
:
1594
(6.4)
Date
solved
:
Monday, January 27, 2025 at 11:23:51 PM
CAS
classification
:
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
\begin{align*} y^{\prime \prime }-6 y^{2}+4 y&=0 \end{align*}
✓ Solution by Maple
Time used: 0.039 (sec). Leaf size: 59
dsolve(diff(diff(y(x),x),x)-6*y(x)^2+4*y(x)=0,y(x), singsol=all)
\begin{align*}
\int _{}^{y}\frac {1}{\sqrt {4 \textit {\_a}^{3}-4 \textit {\_a}^{2}+c_{1}}}d \textit {\_a} -x -c_{2} &= 0 \\
-\int _{}^{y}\frac {1}{\sqrt {4 \textit {\_a}^{3}-4 \textit {\_a}^{2}+c_{1}}}d \textit {\_a} -x -c_{2} &= 0 \\
\end{align*}
✓ Solution by Mathematica
Time used: 0.285 (sec). Leaf size: 373
DSolve[4*y[x] - 6*y[x]^2 + D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
\[
\text {Solve}\left [\frac {4 \left (\text {Root}\left [4 \text {$\#$1}^3-4 \text {$\#$1}^2+c_1\&,2\right ]-\text {Root}\left [4 \text {$\#$1}^3-4 \text {$\#$1}^2+c_1\&,3\right ]\right ) \left (y(x)-\text {Root}\left [4 \text {$\#$1}^3-4 \text {$\#$1}^2+c_1\&,1\right ]\right ) \left (y(x)-\text {Root}\left [4 \text {$\#$1}^3-4 \text {$\#$1}^2+c_1\&,2\right ]\right ) \left (y(x)-\text {Root}\left [4 \text {$\#$1}^3-4 \text {$\#$1}^2+c_1\&,3\right ]\right ) \operatorname {EllipticF}\left (\arcsin \left (\sqrt {\frac {\text {Root}\left [4 \text {$\#$1}^3-4 \text {$\#$1}^2+c_1\&,3\right ]-y(x)}{\text {Root}\left [4 \text {$\#$1}^3-4 \text {$\#$1}^2+c_1\&,3\right ]-\text {Root}\left [4 \text {$\#$1}^3-4 \text {$\#$1}^2+c_1\&,2\right ]}}\right ),\frac {\text {Root}\left [4 \text {$\#$1}^3-4 \text {$\#$1}^2+c_1\&,2\right ]-\text {Root}\left [4 \text {$\#$1}^3-4 \text {$\#$1}^2+c_1\&,3\right ]}{\text {Root}\left [4 \text {$\#$1}^3-4 \text {$\#$1}^2+c_1\&,1\right ]-\text {Root}\left [4 \text {$\#$1}^3-4 \text {$\#$1}^2+c_1\&,3\right ]}\right ){}^2}{\left (4 y(x)^3-4 y(x)^2+c_1\right ) \left (\text {Root}\left [4 \text {$\#$1}^3-4 \text {$\#$1}^2+c_1\&,3\right ]-\text {Root}\left [4 \text {$\#$1}^3-4 \text {$\#$1}^2+c_1\&,1\right ]\right ) \left (\text {Root}\left [4 \text {$\#$1}^3-4 \text {$\#$1}^2+c_1\&,3\right ]-\text {Root}\left [4 \text {$\#$1}^3-4 \text {$\#$1}^2+c_1\&,2\right ]\right )}=(x+c_2){}^2,y(x)\right ]
\]